08 MM1 Variations

08 MM1 Variations - CS-350: Fundamentals of Computing...

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Unformatted text preview: CS-350: Fundamentals of Computing Systems Page 1 of 4Lecture Notes Azer Bestavros. All rights reserved. Reproduction or copying (electronic or otherwise) is expressly forbidden except for students enrolled in CS-350. Variations of the M/M/1 Queuing System In the analysis of the M/M/1 system, we have been concerned with exponential service times. Recall that an exponential distribution is memoryless (i.e. the service time for one customer could be thought of as totally independent of the service time of other customers). What if we relax this condition? What if the service time is NOT exponential? Constant Service Time (i.e. M/D/1 systems) Here we assume that the service time is constant. In other words, all customers require the same amount of service. Examples of constant service time include the transmission time of constant-size cells in ATM networks, or the time it takes to get a single car through a car-wash, etc. One can show that under such assumption we get: +=)1(22q)1(22=wObviously, using Littles formulae, we can estimate Tqand Twas well. General Service Time (i.e. M/G/1 systems) If we do not know the distribution of service time, but we know the normalized value of the service time standard deviation (i.e. the ratio of the service time standard deviation and the service time), then we can use the following formulae that we present without proof. +=2121TsATs+=12Aq=12AwCS-350: Fundamentals of Computing Systems Page 2 of 4Lecture Notes Azer Bestavros. All rights reserved....
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08 MM1 Variations - CS-350: Fundamentals of Computing...

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