4.8 Derivation of expected waiting times The method used in Section 4.9 for deriving the expected waiting time Wbar.gif (557 bytes)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 Wbar.gif (557 bytes)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 Wbar.gif (557 bytes)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 Wbar.gif (557 bytes)qk in a M/M/1 system with preemptive priorities.