| Characteristics
of the System |
|
|
State
|
Total number of customers
in the system; i.e., the number in the queue plus the
number in service |
| |
K
|
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. |
| |
L
|
Expected number of customers
in the system at steady state. |
| |
W
|
Expected time customer
spends in the system at steady state. |
Characteristics of the Arrival Process |
| |
N
|
The size of the
input source. |
| |
|
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
state. |
| |
|
The expected customer waiting time in the queue at steady
state. |
| |
Queue discipline
|
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
are present. |
| |
|
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
is .
|
| |
|
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. |
| Little's
Law for Queuing Systems |
| |
|
Average number = flow rate * residence time
|
