Queuing Model Summary. Assumptions of the Basic Simple Queuing Model. Arrivals are served on a firstcome, firstserved basis (FCFS) Arrivals are independent of preceding arrivals
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=
Average number of units in the system
L
s

1
=
Average time in the system
W
s

2
=
Average number of units in the queue
L
q
(  )
=
Average time waiting in
the queue
W
q
(  )
=
System utilization
Simple (M/M/1) Model EquationsProbability of 0 units in system, i.e., system idle:
=

=

P
1
1
0
Probability of more than k units in system:
( )
k+1
l
=
P
n>k
Where n is the number of units in the system
Simple (M/M/1) Probability EquationsProbability of zero people or units in the system:
Average number of people or units in the system:
Average time a unit spends in the system:
n! = 1 x 2 x 3 x 4 x……..x (n1) x n
n0 = 1; 0! = 1
Average number of people or units waiting for service:
Average time a person or unit spends in the queue
Average number of people or units waiting for service:
Average time a person or unit spends in the queue
Average number of people or units in the system:
Average time a unit spends in the system:
(M/D/1) Equations