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Unformatted text preview: PREEMPTIVE PRIORITY QUEUES Consider an M/M/1 queuing system in which there are two classes of customers--high and low priority--who arrive under independent Poisson processes with parameters of, respectively, 1 and 2 . We assume that: No low-priority customer enters service when any high-priority customers are present. If a low-priority customer is in service, his service will be interrupted at once if a high-priority customer arrives, and will not be resumed until the system is again clear of high-priority customers. Service times for different customers are independent, and all follow an exponential distribution with parameter . We seek here the average queue length and mean time in system for high-priority (hereafter Type 1) customers, and the corresponding quantities for low-priority (Type 2) customers. Easy Start The analysis for L 1 and W 1 (L and W for the Type-1s) is straightforward. Type-2 customers are nonexistent as far as Type- 1 service is concerned, so the Type-1s enjoy an M/M/1 queuing system with arrival 1 and service rate . We can therefore invoke previous results and write: W 1 = 1/( - 1 ) L 1 = 1 /( - 1 ) Light Turbulence Obviously, matters are more complicated for the Type-2 analysis. We proceed first to calculate E 2 (w k 1 ,k 2 ), the conditional k mean time in the system for a Type-2 customer who arrives to find 1 Type-1s and k 2 Type-2s already there....
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This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.
- Fall '06