Question

Consider the following two-server one-queue system from time = 0 to time = 20 min. If both servers are available when a customer arrives, the customer will choose server1. Customers waiting in the queue enter service whenever any one of the two servers becomes available (first come, first serve). Arrivals and service times are: • Customer #1 arrives at t = 0 and requires 2 minutes of service time • Customer #2 arrives at t = 1 and requires 5 minutes of service time • Customer #3 arrives at t = 3 and requires 3 minute of service time • Customer #4 arrives at t = 12 and requires 4 minute of service time Solve for system throughput (X) (# of customers served per unit time during the simulation time), total busy time for server 1(B1), total busy time for server 2(B2), mean service time for server 1(Ts1), mean service time for server 2(Ts2), server 1 utilization (U1), server 2 utilization (U2), average delay in the queue (D), average number of customers in the queue (Q), and average number of customers in the system (L). Also, draw the graph of time vs number of customers in the system. Show your work to receive full credit.

Answer 1

Solution

Simulation Process Total

[Codes used in the following table:

CN: Customer #; AT: Arrival Time; S1: Server 1; S2: Server 2; SR: Service Time;

IT: Idle Time]

CN	AT	Served by		SR	SR (S1)		SR(S2)		IT		Remarks
		S1	S2		ST	ET	ST	ET	S1	S2
1	00	a		2	00	02					*1
2	01		a	5			01	06		1	S1 is busy with C1
3	03	a		3	03	06			1		S2 is busy with C2
4	12	a		4	12	16			6	10	*1
Total				14	00	16	00	16	7	11

*1By the given stipulation that when both servers are free, customer goes to S1.

Answers to the questions:

1) # of customers served per unit time during the simulation time = ¼ ANSWER 1

[4 customers in 16 minutes]

2) Total busy time for server 1(B1) = (2 + 3 + 4) = 9 minutes ANSWER 2

3) Total busy time for server 2(B2) = 5 minutes ANSWER 3

4) Mean service time for server 1(Ts1) = 3 minutes ANSWER 4 [3customers in 9 minutes]

5) Mean service time for server 2(Ts2) = 5 minutes ANSWER 5 [1customer in 5 minutes ]

6) Server 1 utilization (U1) = 56.25% ANSWER 6 [busy 9 minutes over 16 minutes]

7) Server 2 utilization (U1) = 31.25% ANSWER 7 [busy 5 minutes over 16 minutes]

8) Average delay in the queue (D) = 0 ANSWER 8

9) Average number of customers in the queue (Q) = 0 ANSWER 9

10) Average number of customers in the system (L) = ¼ per minute ANSWER 10 [4customers in 16 minutes]

DONE