Question

The following data yields the arrival and service times that each customer will require, for the first 13 customers at a single server queue system (M/M/1). Upon arrival, a customer either enters service if the server is idle or joins the waiting line. When the server completes the work on a certain customer, the next one in line (i.e. the one who has been waiting the longest) enters the service. The studied period ends until the last customer leaves the system

Arrival Times: 12 31 63 95 99 154 198 221 304 346 415 449 526

ServiceTimes: 42355147194851252954407232

(a) Determine the departure times of these 13 customers.

(b) Determine the expected waiting time of customers in the system.

(c) Determine the expected number of customers waiting in the queue and in the system (d) Determine the expected system utilization.

Note that you are expecting to do hand simulation and provide the hand-written solution.

Answer 1

a) departure times of these 13 customers : 54 89 140 187 206 254 305 330 359 413 455 527 567

b) expected waiting time of customers in the system = 1.59

c) number of customers waiting in the queue and in the system = 1.59, 0.71

d) the expected system utilization = 0.9963 x 100 = 99.63%