Consider a special case of an M/G/1 queue with PS scheduling discipline and anarrival

Chapter 9, Problem 1

(choose chapter or problem)

Consider a special case of an M/G/1 queue with PS scheduling discipline and anarrival rate . The Laplace-Stieltjes transform of the service time B is given byLB(s) = b 1s + 1+ (1 b) 1s + 1 2s + 2with 0 b 1. For instance, if b = 0, we have a two-stage hypoexponential dis-tribution (Erlang, if 1 = 2); if b = 1, we have an exponential distribution; andif b = p1 + p2 2/1 (where p1 + p2 = 1), we have a two-stage hyperexponentialservice time distribution. Draw the state diagram of the system, write down thesteady-state balance equations, and proceed to show that the steady-state prob-ability of n jobs in the system has the product-form solution, identical to theM/M/1 FCFS solution.