7. chp 7 waiting line model

8/11/2019 7. Chp 7 Waiting Line Model

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BJQP 2023

MANAGEMENT

SCIENCE


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o Significant amount of time spent in waiting lines

by people, products, etc.

o Providing quick service is an important aspect of

quality customer service.

o The basis of waiting line analysis is the trade-off

between the cost of improving service and thecosts associated with making customers wait.

o Queuing analysis is a probabilistic form of

analysis.

o The results are referred to as operating

characteristics.

o Results are used by managers of queuing

operations to make decisions.

Overview


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o Waiting lines form because people or things arrive at a service faster

than they can be served.o Most operations have sufficient server capacity to handle customers

in the long run.

o Customers however, do not arrive at a constant rate nor are they

served in an equal amount of time.

o Waiting lines are continually increasing and decreasing in length.and

approach an average rate of customer arrivals and an average

service time, in the long run.

o Decisions concerning the management of waiting lines are based on

these averages for customer arrivals and service times.o They are used in formulas to compute operating characteristics of

the system which in turn form the basis of decision making.

Elementsof Waiting Line Analysis


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Waiting lines are commonly found in a wide range of

production and service systems that encounter variable

arrival rates and service times.

First come, first served (FCFS)

Priority Classification


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o Components of a waiting line system includearrivals (customers), servers, (cash

register/operator), customers in line form a waiting

line.

o Customers may also: balking, reneging andjockeying

o Factors to consider in analysis:

o The queue discipline.

o The nature of the calling population

o The arrival rate

o The service rate.

The Single-Server Waiting Line System


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o Assumptions of the basic single-server model:

o An infinite calling population

o A first-come, first-served queue discipline

o Poisson arrival rate

o Exponential service times

o Symbols:

o = the arrival rate (average number ofarrivals/time period)

o = the service rate (average numberserved/time period)

o Customers must be served faster than they arrive (< ) or an infinitely large queue will build up.

Single-Server Waiting Line System

Single-Server Model


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Lq = the average number waiting for service

L = the average number in the system (i.e.,

waiting for service or being served)

P0

= the probability of zero units in the system

= the system utilization (percentage of time

servers are busy serving customers)

Wq = the average time customers must wait for

serviceW = the average time customers spend in the

system (i.e., waiting for service and service

time)


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A customer service counter is a single-server system. If the

arrival rate is 24 customers per hour arrive at checkout

counter and 30 customers per hour can be checked out,

compute:

a) Probability that no customers are in the waiting linesystem

b) Average number in the waiting line system

c) Average number in the waiting line

d) Average time a customer spends in the total queuing

systeme) Average time a customer spends waiting in the queue to

be served

f) Probability that the server is busy

g) Probability that the server is idle


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The multiple-channel model is appropriate whenthese conditions exist:

1. A Poisson arrival rate.

2. A negative exponential service time.

3. First-Come, first-served processing order.

1. More than one server.

1. An infinite calling population.

2. No upper limit on queue length.

3. The same mean service rate for all servers.


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The Student Travel Agency opened 2 countersat DKG 1 to help students purchase bus tickets.Students arrive at the rate of 4 per houraccording to a Poisson distribution and each

counter spends an average 12 minutes for thetransaction.

Determine the operating charateristics (P0, L,

Lq, W, Wqand Pw) for this system.

7. chp 7 waiting line model

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