Example 14.4 Queuing. 14.114.1 | 14.2 | 14.3 | 14.5 | 14.6 | 14.7 |14.8 |14.914.214.314.514.614.714.814.9 Background Information n Which system has the.

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Example 14.4 Queuing

| 14.2 | 14.3 | 14.5 | 14.6 | 14.7 |14.8 | Background Information n Which system has the better steady-state characteristics such as L Sys, W Sys, L Q, and W Q : a single-server system where the single server can serve 30 customers per hour, or a 5-server system where each of the servers can serve 6 customers per hour? n For each system we will, assume that customers arrive according to a Poisson process at rate 25 hour.

| 14.2 | 14.3 | 14.5 | 14.6 | 14.7 |14.8 | Solution n First, note that the two models are comparable in the sense the  fast = s  slow because  fast =30, s=5,  slow =6. n Equivalently, the server utilization is 5/6 for each. n The spreadsheets on the next two slides answer our question. n As you can see, the comparison is not entirely clear- cut.

| 14.2 | 14.3 | 14.5 | 14.6 | 14.7 |14.8 |

| 14.2 | 14.3 | 14.5 | 14.6 | 14.7 |14.8 |

| 14.2 | 14.3 | 14.5 | 14.6 | 14.7 |14.8 | Solution -- continued n The M/M/1 system has a smaller L Sys but a larger L Q. Similarly, it has a smaller W Sys but a larger W Q. n Finally, the M/M/1 system is worse in the sense that is has a smaller percentage of customers who experience no waiting in line and a larger percentage who must wait in lone at least 0.25 hour. n The basic conclusion is that if you hate to wait in a queue, you should prefer the system with multiple slow servers.

| 14.2 | 14.3 | 14.5 | 14.6 | 14.7 |14.8 | Solution -- continued n However, once it is your turn to be served, you will clearly prefer the system with the single fast server. n In this latter system you will spend less total time in the system, but more of it will be spent waiting in line. Take your choice!