Question

1. Consider a single server queueing system. Arrivals take place every four minutes (first arrival takes place at t=0). Service times are random and take the value of 1 with probability 1/2 and 5 with probability ½. Assume that the following service time sequence is generated: S1=5, S2=5, S3=5, S4=1, S5=5. Simulate for T=20 minutes and estimate the average number of customers in the system and the average waiting time of a customer.

Answer 1

Solution

Simulation Process and Relevant Calculations

NOTE: For ease in presentation, following codes are employed.

SN: Simulation #, AN: Arrival #, AT: Arrival time (in minutes), ST: Service Time (in minutes),

SST: Service Start Time (in minutes), SET: Service End Time (in minutes), n: # of customers in the system and w: waiting time (in minutes).

SN	AN	AT	ST	SST	SET	n	w	Notes on n	Notes on w
1	1	00	5	00	05	2	1	AN1 under service, AN2 waiting from 04	AN2 waiting from 04 to 05
2	2	04	5	05	10	2	2	AN2 under service, AN3 waiting from 08	AN3 waiting from 08 to 10
3	3	08	5	10	15	2	3	AN3 under service, AN4 waiting from 12	AN4 waiting from 12 to 15
4	4	12	1	15	16	1	0	AN4 under service, none waiting	none waiting
5	5	16	5	16	21	1	0	AN5 under service, none waiting	none waiting
Total						8	6
Average						1.6	1.2

So, average number of customers in the system = 1.6 Anaswer 1

average waiting time = 1.2 minutes Anaswer 2

DONE