1. Customers entering a shop are served in the order of their arrival by the single server. They arrive in the manner of a Poisson process with intensity, and their service times are independent exponentially distributed random variables with parameter u. By considering the jump chain, show that the expected duration of a busy period B of the server is (μ-2)-1 when λ < . (The busy period runs from the moment a customer arrives to find the server free until the earliest subsequent time when the server is again free.)
1. Customers entering a shop are served in the order of their arrival by the single server. They arrive in the manner of a Poisson process with intensity, and their service times are independent exponentially distributed random variables with parameter u. By considering the jump chain, show that the expected duration of a busy period B of the server is (μ-2)-1 when λ < . (The busy period runs from the moment a customer arrives to find the server free until the earliest subsequent time when the server is again free.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 12EQ:
12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction...
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