The Fundamentals

Collection of entities kept in order Addition of entity at the rear of the terminal

and removal at the front terminal

Used to approximate a real queuing situation to be analyzed mathematically

Allow a number of useful performance measures to be determined: Average number in the queue Average time spent in queue

Population Arrival Service/Servers Queue Output

FIFO (First in First out) LIFO (Last in First out) SIRO (Serve in Random

Order) Priority Queue

Parallel Series

Customers in line

servers

Customers waiting in line

servers

Time Averages:L = expected no. of customers in the systemLQ = expected no. of customers in the queue

LS = expected no. of customers in service

P (all idle) = probability that all servers are idle

P (all busy) = probability that all servers are budy

Customer Averages:W = expected time spent in the systemWQ = expected time spent in the queue

WS = expected time spent in service

λ = average rate at w/c customers enter the system

L = expected number of customers in the systemW = expected time a customer spends in the

system

Therefore:L = λW

LQ = λWQ

LS = λWS

= arrival rate1/= mean time between arrivals

= service rate1/= mean service time per customer

= traffic intensity = / x 100 = % service utilization

Typical Front Desk Queuing:

30 customers per hour Each representative spends 1.5

minutes/customer Manager’s objective is to decide

whether to improve the system or not

30 customers per hour = 0.5 cx/min

1.5 mins/cx = 1 cx / 1.5 mins/cx = 0.67 cx/min

Excel File

M/M/s model M – means that interarrival times are

exponentially distributed M- service times for each server are

exponentially distributed s- denotes the number of servers

Customers arrive at a rate of 150 customers per hour

Branch employs 6 tellers Average service time is 2 minutes to serve each

customer All customers performs all tasks Customers arrived and finds 6 tellers busy

serving First Come First Serve fashion Manager’s objective = to find the “best” numbers

of tellers given that tellers are paid $8 per hour

Thank you