call level qos performance under variable user mobilities in wireless networks
TRANSCRIPT
Mobile Networks and Applications 9, 207–218, 2004 2004 Kluwer Academic Publishers. Manufactured in The Netherlands.
Call Level QoS Performance under Variable User Mobilities inWireless Networks
JELENA MIŠICDepartment of Computer Science, University of Manitoba, Winnipeg, MB, Canada R3T 2N2
YIK BUN TAMDepartment of Computer Science, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Abstract. The concept of adaptive admission control in cellular wireless networks ensures quality of service by reserving bandwidth forhandoff calls. It is equally important in current second generation wireless systems as well as in the future IMT-2000 and UMTS systems.In order to ensure bounded call level QoS we propose to track the changes of the handoff call arrival rate and integrate this information inthe admission algorithm. However, the handoff call arrival rate can vary when the new call arrival rate and/or user mobility vary. In ourprevious work we have analysed bandwidth reservation techniques needed to maintain a stable call level QoS when new call arrival rate ischanging in a group, or groups, of wireless cells. This paper analyses bandwidth reservation techniques that are adaptive to the user mobilityas well as to the changing new call arrival rate, and which can ensure stable call level QoS over a range of user mobilities. We also proposethe technique to derive bandwidth reservation policy when the QoS characteristics over a range of user mobilities are given.
Keywords: cellular wireless networks, IMT-2000, UMTS, adaptive call admission control, quality-of-service
1. Introduction
The cell size of future wireless networks tends to be verysmall, due to the large bandwidth requirements of various net-working services. Due to the user mobility, the number ofcalls crossing the boundary between neighboring cells will belarge. However, a handoff will be unsuccessful if there is in-sufficient bandwidth available in the target cell, in which casethe call will be forced to terminate. The probability of handoffdropping and the forced call termination probability (proba-bility that a call will be terminated due to an unsuccessfulhandoff during its lifetime) are important Quality of Service(QoS) metrics for wireless networks [13]. Hard bounds onhandoff dropping and forced call termination probabilitiesare desirable characteristics both in current second generationwireless cellular systems and in the UMTS and IMT-2000systems. Although this work addresses fixed channel allo-cation (FCA) systems such as GSM and UTRA TD-CDMA[4,9], concept of adaptive bandwidth reservation is portable toWCDMA systems. The key component to achieve guaranteedhard bounds at the call level QoS is in the wireless call admis-sion control algorithm (WCAC). The WCAC algorithm mustreserve enough bandwidth for handoff calls by satisfying thefollowing conditions:
1. It must adapt to traffic intensities in the cells surround-ing the target cell, that is, calls in the surrounding cellsshould cause bandwidth reservation in the target cell toaccommodate their potential handoff to the target cell.
2. It has to provide QoS guarantee for a range of user mo-bility parameters, as different users can have differentspeeds, i.e., different average values of cell residence
times. It is desirable to offer the bound on the forcedcall termination probability to all users regardless of thenumber of the cells traversed during the call’s lifetime.
3. It must prevent hot-spots, i.e., excessive utilization insome cells in the network under non-uniform load. Guar-antees on QoS bounds under a wide range of new callarrival rates in the network are an important property ofthe adaptive WCAC algorithm.
Problems 2 and 3 are related, since the starting point inboth cases is the same bandwidth reservation policy. How-ever, since the new call arrival rate, average call holding time,and average dwell time are independent variables, controllingthe QoS when one of them is changing does not ensure stableQoS when other(s) are variable too.
A number of adaptive WCAC techniques exist in theliterature. Well known approach uses handoff bandwidth es-timation in fixed time periods like [6,11] and [10]. Recently,the adaptive WCAC with handoff load estimation triggered bycertain events such as origination, handoff, and termination ofcalls has been analysed under the conditions of non-uniformnew call arrival rates and homogeneous user mobility [8].The results obtained suggest that the bandwidth reservationproportional only to the utilization in surrounding cells, issufficient to guarantee that the changes of call level QoS willremain small, even under large changes of new call arrivalrates in the group(s) of wireless cells. Therefore, the variableoffered load can be handled by sending the same bandwidthreservation value upon call creation and after each handoff.The absolute value of the QoS is, then, determined by themagnitude of those bandwidth reservation values.
208 MIŠIC AND TAM
This paper focuses on the performance of the adaptiveWCAC based on event-based bandwidth reservation undervarying user mobilities in the wireless network. In this case,the handoff call arrival rate varies with the user mobility and,consequently, the bandwidth reservation rate – if it is to matchthe handoff call arrival rate – must also be made adaptivewith respect to the users’ mobility. Such adaptivity may beachieved by making the bandwidth reservation value am (sentafter mth handoff) dependent on the call handoff dynamics.The series of the bandwidth reservation values am, distrib-uted upon mth handoff, determines the bandwidth reservationpolicy. We first study some intuitive bandwidth reservationpolicies that adapt to the user mobility. Those techniques arefound to offer bounded call level QoS, but their QoS charac-teristics are not controllable by the network operator. Then,we present a technique to develop the bandwidth reservationpolicy satisfying the QoS characteristics given by the networkoperator.
The paper is organized as follows. Section 2 describes theMarkov chain model for wireless cell with admission control.In section 3 the bandwidth reservation process and admissionalgorithm are described. Section 4 presents the analyticalmodel of the admission algorithm under uniform load withvariable user mobility and explains the principles of regulat-ing QoS when user mobility is changing. In section 5 weanalyze two heuristic bandwidth reservation policies, whichare then used in section 6 as the basis for deriving thebandwidth reservation series upon given call level QoS char-acteristics. Section 7 describes the simulation results for QoSbehavior under proposed bandwidth reservation policies. Insection 8 we discuss the assumptions used in the analyticalmodeling throughout the paper and evaluate their impact. Fi-nally, section 9 concludes the paper.
2. System model
Consider a wireless cellular system in which the cells are ofhexagonal shape and arranged in a hexagonal mesh. Due tothe symmetry, each target cell is surrounded with six neigh-boring cells which form a ring around the target cell (they willbe reffered to as the cells from the surrounding ring).
We assume the following:
• The probability of a handoff to any of the six surroundingcells is equal to 1/6.
• The call duration and dwell time are exponentially distrib-uted, with parameters µ and h, respectively.
• The cell capacity is N channels (in subsequent calcula-tions we will use N = 50). Each call consumes onechannel, i.e., 1/N of the total cell capacity.
• Traffic intensity is uniform in all the cells.
The Markov chain that represents the system under an arbi-trary admission algorithm is shown in figure 1. We are awarethat exact modeling of interactions among neighboring cellsrequires a multi-dimensional Markov chain, however we will
Figure 1. Markov chain for a single traffic type, where d = h + µ.
show that results from the one-dimensional model still of-fer useful performance bounds, while keeping the analysiscomparatively simple. The states in the chain represent thenumber of ongoing calls in the target cell. New call arrivalrate is represented by λ. The arrival rates for the handoff callsλh,k depend on the finite user population in the surroundingcells, similar to the Engset model [5]. Under uniform ar-rival rates we observe that high states of the Markov chainin the target cell can be achieved only if the large numberof calls hand-off from the first surrounding ring to the targetcell, therefore leaving smaller number of utilized channels inthe cells from the first surrounding ring. The smaller numberof utilized channels in the cells from first surrounding ringwill result in smaller handoff rate. We assume that the sumof current utilizations of the target cell and the cells from thesurrounding ring is constant and equal to the sum of their av-erage utilizations. In this case, for a target cell with k ongoingcalls, there are 7Nρav − k users in the surrounding ring, withthe “arriving parameter” h giving the handoff call arrival rate:
λh,k = (7ρavN − k)h
6. (1)
The value
M = ρmaxN (2)
is the state where the call admission algorithm starts rejectingnew calls. (We will defer the explanation how the value ρmaxis calculated to a later section of the paper.) Beyond state M ,only handoff calls are accepted. State probabilities of theMarkov chain are then equal to
Pk = ( c6 )k
(A1k
)∑M
i=0(c6 )i
(A1i
) + (A1M )
(A2M )
∑Ni=M+1(
c6 )i
(A2i
) ,
0 � k � M, (3)
Pk =( c
6 )k(A2k
) (A1M )
(A2M )∑M
i=0(c6 )i
(A1i
) + (A1M )
(A2M )
∑Ni=M+1(
c6 )i
(A2i
) ,
M < k � N, (4)
where c = h/(h+µ), A1 = 7Nρav +6λ/h and A2 = 7Nρav.The average utilization and probabilities of new call block-
ing and handoff call dropping for this system are given by
ρav = 1
N
N∑k=0
kPk, (5)
PB =N∑
k=M
Pk, (6)
Phd = PN. (7)
CALL LEVEL QOS PERFORMANCE 209
Note that previous values are functions of λ, λh,k , µ, h, M ,and N .
The average handoff call arrival rate is
λh =N−1∑k=0
Pkλh,k = Nhρav − PhdNh(7ρav − 1)
6. (8)
Since we consider systems with hard bounds on the hand-off dropping probability Phd < 10−2, for large range ofaverage dwell times in micro and pico cellular environment,average handoff call arrival rate can be approximated as λh =ρavNh.
The average cell capacity utilization is
Nρav = λ(1 − PB) + ρavNh − PhdhN(7ρav−1)
6
(µ + h). (9)
By neglecting the last term in the previous expression, thenumber of new calls in the cell can be approximated with
n0 = ρavNµ
h + µ.
Furthermore, the number of calls in the target cell which haveexecuted m handoffs is
nm = n0
(h
h + µ
)m
. (10)
3. Bandwidth reservation for handoff calls: local orneighborhood-based
Handoff call arrivals can be modeled by the Poisson processwith average rate λh. Since handoff call arrivals are random,efficient bandwidth reservation for handoffs should accom-modate their randomness. One way to implement it is to uselocal information in the cell about measured handoff call ar-rival rate as the rate of the bandwidth reservation process.This approach is simple to implement as it requires local in-formation only. However, it can not cope with the variationsof new call arrival rate or users’ mobility, since the informa-tion available is not up-to-date.
The other approach creates bandwidth reservation processin the target cell by using the information about the currentnumber of users in the surrounding cells. If this informationis updated frequently, then bandwidth reservation process re-flects the current state of the handoff call arrival process. Toachieve this, every call that arrives to a cell, either as a newcall or handoff call, will send a bandwidth reservation valueto all the surrounding cells. When a call leaves the cell, thatnumber is cleared from the surrounding cells. Although thispolicy includes additional communication between the basestations, in our work we will adopt it due to the accuracy intracking handoff call arrival process.
The current sum of bandwidth reservation values is kept atthe base station as the average bandwidth reservation rate of
the bandwidth reservation process. Therefore, the bandwidthreservation rate in the target cell is
ν =∞∑
m=0
6nmam, (11)
where nm denotes the number of calls with m executed hand-offs, and am denotes the bandwidth reservation value sentafter mth handoff. After substituting expression (10) in (11),the reservation rate which corresponds to the state k of theMarkov chain is
νk = (7ρavN − k)
∞∑m=0
µ
µ + h
(h
µ + h
)m
am. (12)
Then, the average bandwidth reservation rate becomes
ν =N∑
k=0
Pkνk = ρavN · 6∞∑
m=0
µ
µ + h
(h
µ + h
)m
am. (13)
The average amount of bandwidth reservation values sentout by any connection from the ring surrounding the targetcell is
B = ν
ρavN= 6
∞∑m=0
µ
µ + h
(h
µ + h
)m
am. (14)
Note that due to symmetry and uniform utilization of the cellcapacity, connections from the target cell will send out thesame average amount of bandwidth reservation values.
In the text that follows we shall refer to B as the band-width reservation parameter. If we denote mobility parameterh/(h + µ) = c, the bandwidth reservation parameter B be-comes
B = ν
ρavN= 6(1 − c)
∞∑m=0
am. (15)
In the case when the values of both the mobility parameterc and bandwidth reservation policy am are known, the averagebandwidth reservation rate can be calculated as
ν = ρavNB(c, am). (16)
The bandwidth reservation parameter B depends on themobility parameter of the call, and on the policy for band-width reservation, i.e., on the series of bandwidth reservationvalues am. Equation (15) offers a mechanism to control thebandwidth reservation process through a choice of series am
in order to achieve the required handoff dropping and forcedcall termination probabilities for a given user mobility.
3.1. Meaning of the overload probability in the presence ofbandwidth reservation process
In order to properly reserve the bandwidth for various val-ues of user’s average dwell times and for various boundson handoff dropping probability, we choose the bandwidthreservation values such that the average bandwidth reserva-tion rate is much larger than the handoff call arrival rate. In
210 MIŠIC AND TAM
this case we need a regulating parameter to determine whichportion of the bandwidth reservation rate is needed to achievethe required QoS. We choose this regulating parameter to bethe probability that “the number of the arrivals of the band-width reservation process” will exceed the currently available(residual) capacity of the cell. We call this parameter theoverload probability. If the overload probability is small thismeans that reservation rate is small and/or the residual capac-ity in the cell is moderate to large, so that future handoffs canbe accomodated without dropping. If the overload probabilityis large this means that reservation rate is large and/or residualcapacity is too small to accomodate arrivals of the reservationprocess. This further means that some of the handoffs couldnot be accomodated. By fixing the value of overload probabil-ity to some threshold value PovT, we get admission conditionwhich reserves bandwidth for handoff calls.
Let us first consider the cell at time instant t withinstantaneous utilization ρins and reservation rate νins =(7ρav−ρins)
6 NB. Value N(1 − ρins) denotes the instantaneousresidual capacity of the cell. Then the value of overload prob-ability is equal to
Pov = e−νins
∞∑q=�N(1−ρins)�
νq
ins
q!
= 1
�(N(1 − ρins))
∫ νins
0e−xxN(1−ρins) dx. (17)
We are interested in the moments of time when the thresh-old on overload probability is reached, i.e., when Pov = PovT.If we look at the moments when the threshold is reached inthe very large time interval t ∈ (0,∞), we get the followingexpression:
PovT = 1
�(N(1 − ρmax))
∫ νmax
0e−xxN(1−ρmax) dx, (18)
where ρmax and νmax = NB6 (7ρav − ρmax) denote average
cell capacity utilization and reservation rate at which admis-sion algorithm starts rejecting new calls. Equation (18) showsthat threshold on overload probability PovT corresponds to theadmission threshold on cell capacity utilization. If reserva-tion rate changes either because the new call arrival rate inthe neighborhood of the target cell is changing or becausethe users’ mobility is changing, this will be reflected in thechange of the cell capacity admission threshold. Therefore,reserved bandwidth will always adapt to accomodate inten-sity of the handoff traffic. The purpose of the regulatingparameter PovT is to control the actual value of the handoffdropping probability (and, consequently, the forced call ter-mination probability).
3.2. Admission algorithm based on Pov
We shall illustrate the algorithm using cell (0, 0) from figure 2as the target cell (note that due to the symmetry of the hexag-onal network, any other cell can be considered). The mainsteps of the algorithm are:
Figure 2. Representation of hexagonal cellular network.
1. Variable ν is initialized to zero and current utilization ρinsis set to zero. The values am are chosen according tosome QoS guaranteeing policy.
2. When a new call arrives, the overload probability has tobe calculated using equation (17) in cell (0, 0) and in thesurrounding cells.Pov checking in cell (0, 0): current utilization is incre-mented by 1/N and the overload probability Pov(0, 0) isrecalculated with the new value of ρins. If the updatedvalue is larger than the predetermined limit, the new callis blocked.Pov checking in surrounding cells: In each cell (1, i),0 � i � 5, the value of local ν is incremented by a0and the overload probability is recalculated. If the over-load probability bound in any surrounding cell (1, i) isviolated, the new call must be blocked.
3. The calls which are admitted in cell (0, 0) can freelyhandoff to neighboring cells without invoking the calladmission algorithm again. The handoff call is droppedonly when there is insufficient bandwidth for serving thecall. When a call executes mth handoff from cell (0, 0) toa neighbor cell (1, i), and given that available bandwidthin the cell is sufficient for the call, the following actionsmust be performed:Update load information in cell (1, i): ρins is incre-mented by 1/N , ν is decremented by the bandwidthreservation value am.Update load information in the neighborhood of cells(0, 0) and (1, l): This action consists of the followingsteps:
(a) The new reservation values are distributed to cellssurrounding cell (1, i) and the corresponding valuesof ν are updated. Note that some cells not previouslyincluded in the neighborhood of cell (0, 0) will re-ceive the call’s reservation factor for the first time.This reservation factor will be included in the execu-tion of the admission algorithm for future new callsin these cells.
(b) The cells bordering the cell (0, 0) (which was hostingthe call before the handoff) but which do not belongto the 1-ring neighborhood of the cell currently host-ing the call should delete the appropriate reservationfactor.
CALL LEVEL QOS PERFORMANCE 211
4. When a call terminates, all corresponding bandwidthreservation values in the neighboring cells are deleted andρins in the hosting cell is decremented by 1/N .
4. QoS dependency on mobility parameters
In this section we will determine mobile QoS under variableaverage handoff rates h and variable call departure rates µ.The new call arrival rate is assumed to be nominal new callarrival rate λnom = Nµ (which gives offered load equal toλnom/µ = N Erlangs). The reason for fixing the offered loadto N Erlangs is that we want to focus only on the impact ofvariations of µ and h on the handoff load. However, in realsituations new call arrival rate cannot be controlled and it mayhappen that due to the sudden drop of the call departure ratethe offered load increases beyond the nominal one. This mayoccur in one wireless cell or in the group(s) of cells and cre-ates the situation of nonuniform load in the wireless network.We have treated the problem of call level QoS under nonuni-fom traffic intensities in [8] and have shown that feedbackembedded in the bandwidth reservation rate prevents signifi-cant changes in call level QoS when offered load is increasingeither in one cell or in the group of cells. Therefore, increasesof the offered load beyond nominal load are not of the maininterest in this analysis.
Two important mobile QoS parameters to be consideredare handoff dropping probability and the forced call termi-nation probability. While the handoff dropping probabilityPhd is the probability of one unsuccessful handoff attempt, theforced call termination probability Pfct is the probability thatat least one handoff during the call lifetime will be unsuccess-ful. The later captures the total number of handoffs executedby the call and therefore gives much more information to theuser. Under nominal new call arrival rate the handoff drop-ping probability is determined from (7):
Phd =( c
6 )N(A2N
) (A1M )
(A2M )∑M
i=0(c6 )i
(A1i
) + (A1M )
(A2M )
∑Ni=M+1(
c6 )i
(A2i
) , (19)
where c = h/(h + µ), A1 = 7Nρav + 6N(1 − 1/c), A2 =7Nρav and M = ρmaxN .
The forced call termination probability is determined bythe following expression [13]:
Pfct = Phd
µ/h + Phd= Phd
(1 − 1/c) + Phd. (20)
Note that under nominal load both Phd and Pfct depend onlyon the ratio h/µ, and not on the individual values of h and µ.
Values ρav and ρmax have to be determined by solving thesystem of equations which correspond to the Markov chainpresented in figure 1 and the admission algorithm from sec-tion 3.2, respectively. Markov chain is described by
ρav = 1
N
N∑k=0
kPk, (21)
where Pk’s are the state probabilities of the Markov chaingiven by equations (3) for 0 � k � ρmaxN and (4) forρmaxN < k � N under nominal load.
Call admission algorithm is represented by equation (18)which relates average bandwidth reservation rate and the cellcapacity utilization ρmax at the moment when threshold valueof the overload probability PovT is reached.
The parameters which are not yet determined in the pre-vious equations are mobility parameters h, µ, bandwidthreservation parameter B and pair (ρmax, ρav). Parameters h
and µ (or their ratio) are usually supplied as the propertiesof the call. Furthermore, if the bandwidth reservation pol-icy am is known, then the bandwidth reservation parametercan be calculated, and the system of equations (21), (18) canbe solved for unknown pair (ρmax, ρav). The second (andmore difficult) problem occurs when the bandwidth reserva-tion policy has to be determined such that Phd or Pfct satisfythe required functional relationship on parameter c.
4.1. Principles of regulating QoS when user mobility ischanging
The problem of guaranteeing call level QoS to mobile userswithin wide ranges of average call duration times and celldwell times is to choose the bandwidth reservation policy am
such that Pfct and Phd remain bounded in those ranges. Sincemobile QoS depends only on the ratio c = h/(h + µ) (i.e.,on the ratio of the average call duration time and average celldwell time h/µ), in this work we concentrate on the rangebetween cmin = 0.5 (h = µ) and cmax slightly smaller than 1(which corresponds to large ratios h/µ).
When either handoff rate h increases or the call depar-ture rate µ decreases, while the other parameter is fixed,the user mobility parameter c = h/(h + µ) will increase.In both cases the amount of handoff calls will increase andthe average cell utilization tends to increase. This leads tothe increased handoff dropping probability and forced calltermination probability, which is clearly undesirable. Themechanism is needed which will increase bandwidth reserva-tion when user’s mobility is growing. In this work, mobilitydependent bandwidth reservation is implemented throughbandwidth reservation parameter B. The role of parame-ter B when user’s mobility is changing can be explained usinggraphical representation of equation (18), as shown in fig-ure 3.
The Pov value corresponds to the area below the integrandfunction
f (x) = e−xxN(1−ρmax)
�(N(1 − ρmax))
in the segment x = [0, ν], depicted in figure 3. The functionf (x) has the maximum at x = N(1 − ρmax).
Let us consider the character of changes of average band-width reservation rate
ν = ρavNB
212 MIŠIC AND TAM
Figure 3. Representation of the utilization regulation property of the admis-sion algorithm.
and average handoff call arrival rate
λh = ρavNh
when the user mobility parameter c increases by �c. Theincrease �c can be contributed by both changes of h and µ:
�c = ∂c
∂h�h + ∂c
∂µ�µ = µ�h − h�µ
(h + µ)2 . (22)
We should also note that any change �c can be representedas the equivalent change of �h = ∂h
∂c�c = 1
∂c/∂h�c only (or
�µ only).Therefore, the average handoff call arrival rate will grow
by
�λh = ∂ρav
∂cNh�c + ρavN
∂h
∂c�c. (23)
In the presence of the mobility driven bandwidth reservation,the first component of the expression (23) is negative sinceaverage utilization decreases with the increase of mobility pa-rameter due to the increased bandwidth reservation. Undermoderate bandwidth reservation policies, average utilizationdrops around 25% in the range c = [0.5, 1] which gives aver-age value |∂ρav/∂c| ≈ 0.5. Therefore, the total change �λh
is normally positive since |ρav| > |∂ρav/∂c|µh/(µ + h)2.When the mobility parameter c grows, the average band-
width reservation rate will change due to the changes ofaverage utilization ρav and bandwidth reservation parame-ter B, that is
�ν = N
(∂ρav
∂cB�c + ∂B
∂cρav�c
). (24)
The character of the change �ν depends on the particularbandwidth reservation policy, i.e., on the sign and absolutevalue of ∂B/∂c. Therefore, we have to consider followingcases:
1. (�λh > 0, �ν > 0, �c > 0). In this case, the end of theintegrating segment ν tends to shift to the right towardsthe higher values of Pov. However, Pov regulation main-tained by the admission algorithm has to keep the area be-low the function at the constant value PovT, so it will thenshift the integrand function f (x) in the direction of thechange of reservation rate ν. This means that the point ofmaximum of the integrand function x = N(1−ρmax) willincrease, which is equivalent to the decrease of the value
of ρmax. The shifted function f (x) also gets distortedbut this is negligible for small changes of utilization. De-crease of ρmax will lower the number of admitted calls inorder to decrease the utilization and to cancel the increaseof λh. However, the amount of decrease of threshold uti-lization depends only upon the amount of the increase ofthe bandwidth reservation rate, i.e., on the ∂B/∂c. There-fore, the handoff dropping probability after the change ofthe call mobility depends mostly on ∂B/∂c.
2. (�λh � 0, �ν > 0, �c > 0). In this case the in-crease of �ν as the response to the change �c will bevery large, and this will result in the large decrease ofthe threshold utilization ρmax. As the consequence, largenumber of the new calls will be blocked and the averageutilization will decrease leading to the drop of λh. Thissituation corresponds to the bandwidth over-reservationwhen ∂B/∂c is unnecessary high, i.e., when |ρav| <
|∂ρav/∂c|µh/(µ + h)2.
3. (�λh > 0, �ν � 0, �c > 0). In this case, the end ofthe integrating segment ν tends to shift towards the lowervalues of Pov. In order to keep the value of overloadprobability at level of PovT, the admission algorithm willshift the integrand function f (x) to the same direction asthe change of ν. As the result, the point of maximum ofthe integrand function will decrease, which results in theincrease of the threshold utilization ρmax. As the conse-quence, more new calls will be admitted which furtherincreases the handoff dropping probability, and leads tothe large number of terminated calls.
4. (�λh � 0, �ν � 0, �c > 0). This case is impossi-ble according to the discussion given in the previous twoparagraphs.
Therefore, for the change �c of the mobility parameter,the admission control algorithm will maintain the relationship�ν ≈ N�(1 − ρmax), i.e.:
dν
dc≈ −Ndρmax
dc, (25)
which shows that threshold utilization ρmax is approximatelylinearly proportional to the bandwidth reservation rate ν.
5. Some intuitive bandwidth reservation policies
If bandwidth reservation policy am is known, the value
B = 6K(1 − c)
∞∑m=0
cmam (26)
can be calculated. Constant K is needed to calibrate B to aknown value under given user’s mobility (we use B = 0.237under h/µ = 5, i.e., c = 0.833). In all calculations, wewill assume that network operates at the nominal offered load,λnomµ
= N Erlangs. The threshold for the admission algorithmis set to PovT = 0.5.
CALL LEVEL QOS PERFORMANCE 213
Figure 4. Call QoS behavior with constant bandwidth reservation parame-ter B.
5.1. Fixed bandwidth reservation
If bandwidth reservation values are constant, i.e., am = a0,the bandwidth reservation factor becomes B = 6Ka0. Bysolving equation (26), for calibrating purposes we obtainKa0 = 0.0395.
In this case the change of handoff call arrival rate is equalto
�λh = ∂ρav
∂cNh�c + ρavN
∂h
∂c�c (27)
and the change of reservation rate is
�ν = N∂ρav
∂cB�c. (28)
If the increment of the cell capacity utilization is positive(for �c > 0), then the increment of the reservation rate wouldalso be positive. However, increase of the reservation rateleads to the lower clipping utilization ρmax and therefore tothe lower cell capacity utilization, which directs us to the con-clusion that increment of the cell capacity utilization shouldbe negative. Decrease of the reservation rate when the users’mobility is increasing shows that this policy can not guaranteegood QoS for highly mobile users. Therefore, both handoffdropping probability and the forced call termination probabil-ity will increase with the growth of mobility parameter c asshown in figure 4. The consequence of the increasing forcedcall termination probability under fixed bandwidth reserva-tion scheme is the decreasing average utilization as shown in
Figure 5. New call blocking probabilities: Pb1 for B = 6Ka0, Pb2 forB = 6K/(1 − c) and Pb3 for B = 6K(1 − c)
∑∞m=0 m1/2cm.
figure 4. New call blocking probability is shown as Pb1 infigure 5.
5.2. Prioritizing calls with large number of executed handoffs
Intuitively, mobility-dependent bandwidth reservation couldbe implemented if bandwidth reservation values could some-how grow with the number of executed handoffs. Suchapproach will increase bandwidth reservation in two cases:
1. Calls with short dwell times and moderate duration timeswill increase bandwidth reservation according to theirmobility dynamics.
2. Very long calls with moderate dwell times will imple-ment the “call aging” concept to decrease the probabilityof forced termination when call has already executed anumber of handoffs.
Two representatives of these bandwidth reservation poli-cies will be shown. The first one is
B = 6K(1 − c)
∞∑m=0
(m + 1)cm = 6K
1 − c. (29)
The calibration constant K is needed, and it is set to matchthe tuple (c = 5/6, B = 0.237). Figure 6 shows computedcall level QoS. However, from this figure we note that Pfct isbounded, but not flat.
Figure 7 shows QoS with B = 6K(1 − c)∑∞
m=0 m1/2cm.Both of these policies can be classified as (�λh > 0, �ν >
0, �c > 0). These policies are easy to implement, sincethey only require the handoff counter to be maintained at themobile terminal. The value of the handoff counter should besent to the target base station after the handoff. Target basestation will apply the appropriate function (square root) anddistribute the value to the surrounding base stations.
Figures 6 and 7 show that Pfct and Phd are bounded forvariable but homogeneous users’ mobility. New call block-ing probabilities for these two cases are shown in figure 5 asPb2 and Pb3, respectively. We observe that under high users’mobilities, the second policy offers lower new call blockingprobability while keeping the forced call termination proba-bility bounded.
214 MIŠIC AND TAM
Figure 6. Call QoS behavior with bandwidth reservation parameter B =6K/(1 − c).
Figure 7. Call QoS behavior with bandwidth reservation parameter B =6K(1 − c)
∑∞m=0 m1/2cm.
6. Deriving the bandwidth reservation policy upon givenQoS characteristics
Although intuitively chosen bandwidth reservation policiesoffer bounded call level QoS we are not free to choose theshape of the mobile call level QoS accross the range of users’mobilities. The next step in investigating bandwidth reserva-tion policies is to develop bandwidth reservation series whichwill result in certain QoS characteristics requested by the net-work operator. The problem of controlling call level QoSwhen the user mobility is changing can be defined as fol-lows:
• Determine the bandwidth reservation policy am which willoffer
Pfct = χ(c) (30)
(or Phd = ψ(c) = (1/c − 1)Pfct/(1 − Pfct)) when themobility parameter c changes in the range 0.5 � c < 1.
The first approach to find the suitable bandwidth reserva-tion policy requires solving of the system of equations (18),(21), (30) for the variables ρav, ρmax, B for the number of mo-bility parameters in the range c ∈ [0.5..1]. Due to the largecomplexity of the problem, the solutions had to be obtainednumerically. When the set of the values for the bandwidthreservation parameter are known, regression technique can beused to transform the set of points [c, B] to the appropriatefunction B(c). For example, for χ(c) = const we solved thesystem for 42 values of c and obtained B as the rational func-tion of c. After that, B(c) is transformed into partial fractionsand then into the series B(c) = 6(1 − c)
∑∞m=0 cmam. The
job of computing the values of am should be done offline bythe network operator and stored in the mobile terminal whenit is powered up.
In order to overcome complexity of numerical solutionsand regression, in this section we will derive approximateanalytical expression for the bandwidth reservation parame-ter B(c) when the control function χ(c) is given. We willassume that flat forced call termination porobability is re-quested, i.e., χ(c) = const. This approach will give us betterunderstanding of the role of the bandwidth reservation policyunder changing mobility.
We analyze the derivatives of the system of equations (21),(18), (30) under nominal new call arrival rate. Those deriv-atives can be obtained by considering state probabilitiesPk given in (3) and (4) as Pk(ρav, ρmax, c) and Pov asPov(ν(ρav, B), ρmax):
dρav
dc= 1
N
N∑k=0
k∂Pk
∂ρav
dρav
dc
+ 1
N
∂(∑N
k=0 kPk)
∂ρmax
dρmax
dc+ 1
N
N∑k=0
k∂Pk
∂c, (31)
∂Pov
∂ν
∂ν
∂c+ ∂Pov
∂ρmax
∂ρmax
∂c= 0, (32)
ψ ′(c) = ∂PN
∂ρav
dρav
dc+ ∂PN
∂ρmax
dρmax
dc+ ∂PN
∂c. (33)
CALL LEVEL QOS PERFORMANCE 215
Figure 8. Full and partial derivatives for ρav and ρmax with bandwidth reser-vation parameter B = 6K/(1 − c).
Since ν = ρavNB, and by applying approximation (25),equation (32) becomes(
ρavdB
dc+ dρav
dcB
)+ dρmax
dc= 0. (34)
Furthemore, since from intuitive bandwidth reservationpolicies it results that |ρav∂B/∂c| � |(dρav/dc)B|, the previ-ous expression will be simplified to
ρavdB
dc≈ −dρmax
dc(35)
and the system of equations (31) and (33) with (34) becomes
dρav
dc
(1 − 1
N
N∑k=0
k∂Pk
∂ρav
)
= −ρav1
N
∂(∑N
k=0 kPk)
∂ρmax
dB
dc+ 1
N
N∑k=0
k∂Pk
∂c, (36)
∂PN
∂ρav
dρav
dc− ρav
∂PN
∂ρmax
dB
dc+ ∂PN
∂c− ψ ′(c) = 0. (37)
By careful study of the corresponding partial derivativesfor the intuitive bandwidth reservation policies as shown infigure 8, we find that 1
N
∑Nk=0 k ∂Pk
∂cis negligible compared to
the other two partial derivatives, and also that
1N
∂(∑N
k=0 kPk)
∂ρmax
1 − 1N
∑Nk=0 k
∂Pk
∂ρav
≈ 1.
After this simplification, we obtain two differential equa-tions:
dρav
ρav= −B ′(c)dc, (38)
dB
dc=
∂PN
∂c− ψ ′(c)
ρav(∂PN
∂ρav+ ∂PN
∂ρmax). (39)
The solution of the first one is ρav(c) = K1 exp(−B(c)),and since −dρmax/dc ≈ ρavdB/dc, we obtain ρmax(c) =ρav(c)+K2. Constants K1 and K2 are determined by solvingthe system of equations (18), (21), (30) for one value c = c1.
The last differential equation left is equation (39). Aftersubstitution of ρav(c) and ρmax(c) it has the form dB/dc =f (B(c), c). By repetitive differentiation and substitution ofvalues c = c1, B = B(c1) the series of derivatives ofdnB(c)/dcn is obtained, so the function B(c) is approximatedwith the Taylor series:
B(c) = B(c1) + dB
dc(c − c1) + 1
2!dB
dc(c − c1)
2 + · · · . (40)
By further equating the series (40) with (15) correspondingvalues for am are obtained. They closely match the val-ues obtained by numerical solutions of equations (18), (21),(30). For Pfct = 0.01, first 20 bandwidth reservation values(a0, . . . , a19) are:
(−.00133, .00758, .01941, .03109, .04150, .05034,
.05766, .06365, .06851, .07244, .07561, .07816,
.08021, .08186, .08319, .08426, .08511, .08580,
.08636, .08680).
Bandwidth reservation values in this case should be keptat the base stations since they do not depend on the user’sspeed or the call holding time. The mobile terminal shouldonly maintain handoff counter and send its value to the targetbase station after the handoff. Target base station will furtherdistribute it to the base stations in the surrounding cells. Notethat bandwidth reservation values after a15 are growing veryslow, so storing 20 values should be sufficient.
7. Simulation results on QoS bounds with changingmobility
In this section we present results of the simulation carriedout in order to verify analytical models for the two proposedbandwidth reservation policies, and to verify am values ob-tained for required flat forced call termination probability.Our goal here is to show that through the use of different se-ries of reservation values, both the magnitude of the forcedcall termination probability and its correlation to the mobil-ity factor c = h/(µ + h) can be easily controlled. Statisticswere collected in the central cell. In each simulation experi-ment the cells are uniformly loaded with nominal load of 50Erlangs. The call duration was exponentially distributed withthe average of 1/µ = 500 seconds. In each set of experi-ments the dwell time was also exponentially distributed andthe average 1/h varied such that the mobility factors werec = 0.5, 0.6, 0.7, 0.8, 0.833 and 0.9. In other words, eachcall made from one (c = 0.5) to ten handoffs (c = 0.9) onthe average during its lifetime. The PovT threshold in the ex-periments was 0.5. The size of the simulated cellular networkis 9 rings.
In the first simulation experiment, we tested the flat band-width reservation policy, i.e., am = a0 for any m =
216 MIŠIC AND TAM
Figure 9. Simulated call QoS behavior with constant bandwidth reservationparameter B.
1, 2, 3, . . . . The series was calibrated at the point PovT = 0.5and B = 0.237. The implication of this policy is that thenumber of reserved channels is almost constant with respectto c. As the mobility increases and the number of reservedchannels stays the same, the handoff dropping probability in-creases exponentially (see figure 9). This shows that a trunkreservation policy that reserves a fixed number of channelsfor handoffs is unsatisfactory for the mobile users with vary-ing mobility.
In the second experiment we used a series am determinedin section 6 that gave a flat upper bound on the forced calltermination probability. The calibration point was Pfct = 1%and PovT = 0.5. The results obtained from the simulationshave shown that the calibrated upper bound was maintainedby the admission policy (see figure 10) except for the verylow value of user mobility.
While the property of having a flat upper bound on Pfct ishighly desirable, storing of bandwidth reservation values inthe memory of the mobile terminal may not be convenient.Also, a user’s mobility may change suddenly. For example, auser is stationary when he is waiting for a taxi, but moves at ahigh speed once he gets on the taxi. It is easier to give a hinton the user’s mobility by the number of successful handoffshe has made. A fast moving user will make more handoffs
Figure 10. Simulated call QoS behavior with required flat Pfct, λ = 0.1,c = h/(h + µ), µ = 0.002.
during his call’s lifetime than a slow moving or stationaryone. Therefore, by using a series of reservation values am
that increases with m, we can reserve more bandwidth forfast moving users and provide satisfactory QoS to them. Inthe experiments, we tested two series am = K(m + 1) andam = K
√m, where K is a calibration constant. The series
were calibrated at c = 5/6, B = 0.237 and PovT = 0.5. Itcan be seen that we can easily control the trend of Pfct withrespect to c through different series that are functions of m
(see figures 11 and 12). The absolute values of the Pfct canbe tuned by using different calibration constant K . A largeK causes more channels to be reserved, thus leading to lowerPfct. Conversely, a small K leads to higher Pfct.
8. Evaluation of the effects of the assumptions used in theanalytical modeling of the proposed CAC undervariable user mobility
In this section we discuss some of the assumptions we haveused in modeling the proposed CAC and their impact.
Exponential distribution of call holding and dwell time.Although exponential distribution approximations of thecell residence time and call holding time offer a sim-
CALL LEVEL QOS PERFORMANCE 217
Figure 11. Simulated call QoS behavior with bandwidth reservation parame-ter B = 6K/(1 − c), λ = 0.1, c = h/(h + µ), µ = 0.002.
ple way to model the performance of Mobile Comput-ing/Personal Communication Systems (MC/PCS), in re-ality both the dwell time and call holding time are moreaccurately approximated with sub-exponential distribu-tions such as Erlang or Gamma distributions [2,3]. In[12] unencumbered call holding time and dwell time aremodeled using sums of hyperexponential (SOHYP) vari-ables. The most important consequence of exponentialsimplification is that, the handoff call arrival rate (and,consequently, the handoff call dropping probability) areunderestimated compared to the sub-exponential modelwhile they are slightly overestimated compared to SO-HYP model. Yet in our scheme, the bandwidth reservationrate in the target cell is formed from the current popula-tion of mobile terminals in the surrounding ring, and itshould accurately reflect the distribution of the call holdingtimes and dwell times. Therefore, the reserved bandwidthalways matches the current intensity of the handoff call ar-rival rate.
Total symmetry of the network and uniform directionalprobabilities. The proposed bandwidth reservation scheme
should also perform well under strong directional proper-ties of the users, even in cases where the network is nota perfect hexagonal mesh. This is due to the fact that
Figure 12. Simulated call QoS behavior with bandwidth reservation parame-ter B = 6K(1 − c)
∑∞m=0 m1/2cm, λ = 0.1, c = h/(h + µ), µ = 0.002.
the cells along the main paths of the mobile terminalswill receive the largest amount of the bandwidth reserva-tion values. In such cases, however, smaller values of theQoS tuning parameter PovT should be used along the mainpaths. Namely, the bandwidth reservation rate in the targetcell is contributed mostly by the mobiles which will exe-cute handoff to the target cell, whereas in the symmetriccase only one-sixth of the mobiles that have sent reser-vation value will execute the handoff to the target cell.Therefore, the bandwidth reservation rate in the strong di-rectional case is smaller than in the symmetric case andthis should be compensated for by assigning smaller val-ues to the overload probability threshold. Consequently,the amount of resources reserved will suffice to accomo-date handoffs along the main paths.
Uniform traffic load in all the cells. In this work we focuson the variable users’ mobility and assume a uniform traf-fic intensity in all cells. However, the proposed bandwidthreservation performs well even under non-uniform arrivalrates of new calls in the network. This is due to the fact thatinformation about emerging hot-spots is promptly commu-nicated to the neighboring cells through the growth of thebandwidth reservation rate, which is directly proportionalto the utilization in the hot-spot. Henceforth, the cells
218 MIŠIC AND TAM
surrounding the hot-spot area will limit the admission ofnew calls in order to accommodate handoffs from the hot-spot(s). (Note that we addressed the problem of hot-spotsin [8].)
Current utilization of the considered group of cells isconstant. Exact modeling of the interactions among the cells
requires the use of a multidimensional Markov chain.However, in order to keep the model tractable, we retainedthe one-dimensional Markov chain model of the cell, whilestill being able to model interactions among the neighbor-ing cells through the handoff call arrival rate in the cell. Tothat end, under uniform load the current sum of utilizationsof the target cell and its first surrounding ring is assumedto be equal to the sum of their average utilizations. Wefound that this approximation gives a better fit with thesimulation results than the (simpler and, hence, less real-istic) assumption that each cell surrounding the target celloperates at its average utilization.
9. Conclusion
This paper has analysed adaptivity to the user mobility inthe admission control in cellular wireless networks. It pro-poses bandwidth reservation policies which are adaptive tothe changes in user mobility, so that handoff dropping proba-bility and forced call termination probability remain bounded.Furthermore, it proposes technique to derive bandwidth reser-vation policy which satisfies required call level QoS. Sincewe have observed in [8] that constant bandwidth reservationpolicy successfully copes with changes in the new call arrivalrates, we conclude that mobility driven bandwidth reservationis a technique capable to maintain required call level QoSwhen both new call arrival rates and user mobility are vari-able.
Although this work covers fixed number of channels percell, adaptive bandwidth reservation can be also integratedin 3G WCDMA systems through adaptive power interferenceestimation and careful addressing of soft handoff issues.
Acknowledgement
The authors would like to thank the anonymous reviewersfor their constructive comments which helped us improve thequality of the paper.
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Jelena Mišic received her Ph.D. degree in computerengineering 1993, from University of Belgrade, Yu-goslavia. From 1995 to 2003 she was with HongKong University of Science and Technology. Shejoined University of Manitoba in 2003 where she isan Associate Professor. Her current research interestincludes wireless networks and mobile computing.She is the member of IEEE Computer Society.
Yik Bun Tam received his Mphil degree in com-puter engineering from the Hong Kong University ofScience and Technology (HKUST), Hong Kong, in2000. He is currently working in Hong Kong.