08SimHw1sol - IEOR 4404 Simulation Prof Mariana...

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IEOR 4404 Assignment #1 Solutions Simulation October 2, 2008 Prof. Mariana Olvera-Cravioto Page 1 of 4 Assignment #1 Solutions 1. (a) To compute the departure times of the 13 customers, we proceed as follows. First note that A 1 = 12 and S 1 = 40. Thus, the first customer arrives at time t = 12 and stays in service until time t = 52. At t = A 2 = 31, another customer arrives and joins the queue (which now consists of exactly one customer), since she cannot be served immediately. At t = 52, the server becomes empty again and customer 2 starts her service which ends at t = 52 + 32 = 84, at which time she leaves service. In the meantime, at t = 63, another customer has arrived and joined the queue. Her time of entry into service is t = 84 and subsequent departure is at t = 84 + 55 = 139 ... etc. Proceeding as such, the departure times are: 52 , 84 , 139 , 187 , 205 , 255 , 302 , 320 , 348 , 402 , 451 , 527 , 549 (b) Paralleling the same logic as in part (a), we get that the departure times when there are two servers in the system are: 52 , 63 , 118 , 143 , 136 , 204 , 245 , 239 , 332 , 400 , 451 , 527 , 549 (c) We now consider a different service mechanism: upon completion of service of the cus- tomer in the server, the next customer to enter service is the one who has been waiting the least amount of time. To compute the departure times, we need to proceed exactly as before, except we should also keep track of the waiting times of the customers waiting in line, and have the next entry into service be that of the customer who has been waiting the least amount of time. The departure times are given by: 52 , 84 , 139 , 320 , 157 , 207 , 254 , 272 , 348 , 402 , 451 , 527 , 549 2. (a) Note that D 0
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