Question

Problem 1 Given the data below for a single-server single-queue system, find the following performance measures. Customer Arrival Time Service Time (min) Time Customer Waits in Queue (min) Time Customer spends in System (min) Idle Time of Server (min) 04 0) Average Waiting Time (11) Probability of a customer to be waiting (i.e., number of waiting customers over total number of customers) (II) Probability of idle server (i.e., proportion of idle time over total running time) (iv) Average Service Time (v) Average Time between Arrivals (i.e., interarrival times) (vi) Average Waiting Time of those waiting (vii) Average Time a customer spends in the system

Answer 1

Customer #	Arrival time	Service time	Waiting time	Time in system	Idle time	Interarrival time
1	0	4	0	4	0
2	8	1	0	1	4	8
3	14	4	0	4	5	6
4	15	3	3	6	0	1
5	23	2	0	2	2	8
6	26	4	0	4	1	3
7	34	5	0	5	4	8
8	41	4	0	4	2	7
9	43	5	2	7	0	2
10	46	3	4	7	0	3
Average		3.5	0.9	4.4	1.8	5.11

(i) Average waiting time = 0.90 minutes

(ii) Prob(customers waiting) = 3/10 = 30%

(iii) Prob(idle server) = total idle time / total run time = (1.8*10) / 46 = 0.39

(iv) Average service time = 3.5 minutes

(v) Average time between arrivals = 5.11 minutes

(v) Average time in the system = 4.4 minutes

Computations:

в Customer # Arrival time Service time Waiting time Time in system Idle time Interarrival time + m + tim =C4-C3 C5-C4 =C6-C5 =C7-C6 =C8-C7 =C9-C8 =C10-09 =C11-C10 =C12-C11 =AVERAGE(D3:012) =AVERAGE(E3:E12) =AVERAGE(F3:F12) =AVERAGE(G3:G12) AVERAGE(H4:H12) 12 13 Average