Conversely if s the mms queue is transient why is this

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: in equilibrium has a shifted geometric distribution so L= 1 1 /µ 1= µ µ µ µ = µ By our fourth queueing equation, (3.6), the server’s busy periods have mean ✓ ◆ ✓ ◆ 1 1 1 µ 1 EB = 1= 1= ⇡ (0) µ µ which agrees with (4.20). Example 4.24. M/M/1 queue with a finite waiting room. In this system customers arrive at the times of a Poisson process with rate . Customers enter service if there are < N individuals in the system, but when there are N customers in the system, the new arrival leaves never to return. Once in the system, each customer requires an independent amount of service that has an exponential distribution with rate µ. Lemma 4.7. Let Xt be a Markov chain with a stationary distribution ⇡ that satisfies the detailed balance condition. Let Yt be the chain constrained to stay in a subset A of the state space. That is, jumps which take the chain out of A are not allowed, but allowed jumps occur at the original P rates. In symbols, q (x, y ) = q (x, y ) if x, y 2 A and 0 otherwise. Let...
View Full Document

This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.

Ask a homework question - tutors are online