Analysis of polling models with a self-ruling server

Abstract

Polling systems are systems consisting of multiple queues served by a single server. In this paper, we analyze polling systems with a server that is self-ruling, i.e., the server can decide to leave a queue, independent of the queue length and the number of served customers, or stay longer at a queue even if there is no customer waiting in the queue. The server decides during a service whether this is the last service of the visit and to leave the queue afterward, or it is a regular service followed, possibly, by other services. The characteristics of the last service may be different from the other services. For these polling systems, we derive a relation between the joint probability generating functions of the number of customers at the start of a server visit and, respectively, at the end of a server visit. We use these key relations to derive the joint probability generating function of the number of customers and the Laplace transform of the workload in the queues at an arbitrary time. Our analysis in this paper is a generalization of several models including the exponential time-limited model with preemptive-repeat-random service, the exponential time-limited model with non-preemptive service, the gated time-limited model, the Bernoulli time-limited model, the 1-limited discipline, the binomial gated discipline, and the binomial exhaustive discipline. Finally, we apply our results on an example of a new polling discipline, called the 1 + 1 self-ruling server, with Poisson batch arrivals. For this example, we compute numerically the expected sojourn time of an arbitrary customer in the queues.

Polling Systems and Their Application to Telecommunication Networks

“…Van Ommeren et al [39] consider a polling model with self-ruling service. A server can decide to leave a queue independent of the queue length and the number of served customers.…”

Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue

“…One of the first papers having this property that is similar to model I is [8], where a single server visits a finite number of stations for fixed time periods. More recent queueing models with a single sever visiting multiple queues in a non-work-conserving matter have been studied in [9][10][11][12][13]. In our earlier paper [14], model I was introduced in a more general setting than in this paper.…”