E the ow conservation idea 6 special case mm1 queue an

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Unformatted text preview: at the steady-state equations, since anything out of a state should some up to anything coming in, i.e. the “flow conservation" idea.] 6. Special case: M/M/1 Queue An important special case of B-D process is the case where transition rates are state independent and are fixed, one for birth another for death, i.e., = j = : j For this example, due to Poisson property (we will visit shortly), the interarrival time is exponentially distributed with mean 1= and the service time is exponentially distributed with mean 1=. Also,  known as the average arrival rate. Remember, we are still talking about Markov chains. This is a special case and is identified as the M/M/1 queue (known as Kendall’s notation) where first M is for the arrival, the second M is for the service time and the third entry is to denote we have one server. The state-transition diagram can be shown as below: λ 0 1 µ CS 522, v 0.94, d.medhi, W’99 λ λ 3 2 µ •• • µ 11 For this special case, we g...
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