Priority Queues with Feedback

Abstract

A priority queuing system m which a customer can feed back and change priority after being served is analyzed. More exactly, there are c customer types. Customer type i feeds back after service N(I) -1 times. The kth time a type / customer is m the queue it has priority level f(t, k) and requires a service time with arbitrary distribution G,k Type ~ customers enter from outside as a Poisson process w~th rate X, and can be e~ther preemptive or nonpreemptlve. A customer who has been preempted must start serwce over from the beginning w~th a new (independently chosen) service Ume. The analysis gwes mean waiting times for each customer type at each stage m its itinerary, the mean number of each customer type m the system, and other quantities of interest. It ~s also shown that bulk arrivals and branching can be included m the model without substantially changing the form of the solution.