Sample path methods in the control of queues

Longest Path in Networks of Queues in the Steady-State

Due to the importance of longest path analysis in networks of queues, we develop an analytical method for computing the steady-state distribution function of longest path in acyclic networks of queues. We assume the network consists of a number of queuing systems and each one has either one or infinite servers. The distribution function of service time is assumed to be exponential or Erlang. Fu...

SOME GENERALIZATIONS OF WEAK CONVERGENCE RESULTS ON MULTIPLE CHANNEL QUEUES IN HEAVY TRAFFIC.

This paper extends certain results of Iglehart and Whitt on multiple channel queues to the case where the inter-arrival times and service times are not necessarily identically distributed. It is shown that the weak convergence results in this case are exactly the same as those obtained by Iglehart and Whitt

A sample path analysis of M/GI/1 queues with workload restrictions

A simple random time change is used to analyze M/GI/1 queues with workload restrictions. The types of restrictions considered include workload bounds and rejection of jobs whose waiting times exceed a (possibly random) threshold. Load dependent service rates and vacations are also allowed and in each case the steady state distribution of the workload process for the system with workload restric...

SAMPLE PATH LARGE DEVIATIONS FOR QUEUES WITH MANY INPUTS 1 By Damon

A Note on the Stability of the Many - Queue Head - of - the - LineProcessor - Sharing System with Permanent CustomersAndreas

We consider a single server system consisting of n queues with diierent types of customers and k permanent customers. The permanent customers and those at the head of the queues are served in processor-sharing by the service facility (head-of-the-line processor-sharing). By means of Loynes' monotonicity method a stationary work load process is constructed and using sample path analysis general ...