Page 129 - DCAP601_SIMULATION_AND_MODELING

Unit 8: Simulation of Queuing System (II)

Notes
Example: For the 10 jobs in Example 1
1. Average interarrival time is r = a /n = 320/10 = 32.0 seconds per job
n
2. Average service is s = 34.7 seconds per job
3. Arrival rate is 1/r 1/4 0.031 jobs per second
4. Service rate is 1/s 1/4¼ 0.029 jobs per second
The server is not quite able to process jobs at the rate they arrive on average.

The average delay and average wait are defined as:
n n
1 1
d   d i w   w i
n n
i 1 i 1
Recall w = d + s for all i
i i i
n n n n
1 1 1 1
i 
w   w   (d  s i )   d  s  d  s
i
i
i
n n n n
i 1 i 1 i 1 i 1
Sufficient to compute any two of w, d, s.
Time-averaged Statistics
1. Time-averaged statistics: defined by area under a curve (integration)
2. For SSQ, need three additional functions
(a) l(t): number of jobs in the service node at time t
(b) q(t): number of jobs in the queue at time t
(c) x(t): number of jobs in service at time t

3. By definition, l(t) = q(t) + x(t).
4. l(t) = 0, 1, 2, . . .
q(t) = 0, 1, 2, . . .

x(t) = 0, 1
5. All three functions are piece-wise constant

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