4.8 Derivation of expected waiting times The method used in Section 4.9 for deriving the expected waiting time _qk for class k users of a M/G/1 system with nonpreemptive priorities is very helpful for many problems involving various queue disciplines or priorities.

a. Use this method to derive an expression for _q, the expected waiting time at a M/G/1 system with a last-come, first-served (LCFS) queue discipline. Assume infinite queue capacity. Your result should of course be the same as (4.81), the expression for 17V, for a M/G/1 system with FCFS queue discipline.

b. Use this method to derive expressions (4.111) and (4.112) for _qk in the

case of a M/M/m queueing system with nonpreemptive priorities.

c. Use the same method for deriving expression (4.113) for _qk in a M/M/1 system with preemptive priorities.