Total number of customers
in the system; i.e., the number in the queue plus the
number in service
The maximum number
in the system. When the maximum number in the system is
finite and this number has been reached, an arriving customer
"balks" and does not enter.
Probability of n customers in the system at steady state.
Expected number of customers
in the system at steady state.
Expected time customer
spends in the system at steady state.
Characteristics of the Arrival Process
The size of the
The arrival rate or the expected number of arrivals per
unit time when n
customers are in the system.
The arrival rate when the state of the system does not
affect the rate of customer arrivals. The expected time
between arrivals is .
The average arrival rate when the state of the system
affects the rate of arrival.
Characteristics of the Queue
Maximum number in the queue
The maximum number in the system less the number of servers; K - s.
The expected number of customers in the queue at steady
The expected customer waiting time in the queue at steady
The rule by which customers
are chosen from the queue to receive service. Possible
rules are first-come-first-served, last-come-first-served,
or selection by some priority rule. Unless otherwise stated,
it is assumed that customers form a single queue even
if there are multiple service channels.
Characteristics of the Service Process
Number of service channels.
All are assumed to be identical.
Expected number in service at steady state.
The expected customer service time ()
Mean service rate for the system when n customers
The mean service rate for a single busy server when the
number in the system does not affect the service rate.
The expected time to complete a single service activity
Traffic intensity. This is the ratio between the rate
at which arrivals attempt to use the system and the maximum
service rate of the system.
Efficiency or utilization.
The ratio between the average number of customers in service
and the number of servers.
Law for Queuing Systems
Average number = flow rate * residence time
Operations Research Models and Methods
by Paul A. Jensen
Copyright 2004 - All rights reserved