Piecewise linear test functions for stability and instability of queueing networks
We develop the use of piecewise linear test functions for the analysis of stability of multiclass queueing networks and their associated fluid limit models. It is found that if an associated LP admits a positive solution, then a Lyapunov function ...
Polling systems in heavy traffic: Exhaustiveness of service policies
We study the expected delay in cyclic polling models with general ‘branching-type' service disciplines. For this class of models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the ...
Branching/queueing networks: Their introduction and near-decomposability asymptotics
A new class of models, which combines closed queueing networks with branching processes, is introduced. The motivation comes from MIMD computers and other service systems in which the arrival of new work is always triggered by the completion of former ...
Tail probabilities for M/G/\infty input processes (I): Preliminary asymptotics
The infinite server model of Cox with arbitrary service time distribution appears to provide a large class of traffic models - Pareto and log-normal distributions have already been reported in the literature for several applications. Here we begin the ...
The joint distribution of sojourn times for a customer traversing an overtake–free series of queues: The discrete time case
We investigate a cycle of Bernoulli servers in discrete time. We show that the joint distribution of a customer's sojourn times at the nodes during a round trip is of product form and can explicitly be written down. The results are used to prove ...
Order statistics applications to queueing and scheduling problems
We prove several basic combinatorial identities and use them in two applications: the queue inference engine (QIE) and earliest due date rule (EDD) scheduling. Larson (1990) introduced the QIE. His objective was to deduce the behavior of a multiserver ...
Vacations in GI^X/M^Y/1 systems and Riemann boundary value problems
We consider systems of GI/M/1 type with bulk arrivals, bulk service and exponential server vacations. The generating functions of the steady-state probabilities of the embedded Markov chain are found in terms of Riemann boundary value problems, a ...
