EURO 2024 Copenhagen
Abstract Submission

EURO-Online login

1214. Completion Times of Jobs on Two-State Service Processes and Their Asymptotic Behavior

Invited abstract in session WA-39: Stochastic Models in Service Operations II, stream Stochastic Modelling.

Wednesday, 8:30-10:00
Room: 35 (building: 306)

Authors (first author is the speaker)

1. Melike Baykal-Gursoy
Industrial and Systems Engineering, Rutgers University

Abstract

We consider a repairable service system in which a server experiences randomly occurring service interruptions during which the server works slowly. Every service-state change preempts the task that is being processed. The server may then replace the task with a different one, or it may repeat the same task from the beginning, under the new service-state. We study the completion time of a task under the last two cases as a function of the task size distribution, the service interruption frequency/severity, and the repair frequency. We derive closed form expressions for the completion time distribution in Laplace domain under replace and repeat recovery disciplines and present their asymptotic behavior. In general, the heavy tailed behavior of completion times arrises due the heavy tailness of the task time. However, in the preempt- repeat service discipline, even in the case that the server still serves during interruptions albeit at a slower rate, completion times may demonstrate power tail behavior for exponential tail task time distributions. Furthermore, our results reveal that the stationary first order moments, i.e., expected completion time, expected number in the system in infinite server queues with Markov modulated service processes are insensitive to the way the service modulation affects the servers, system-wide modulation affecting every server simultaneously vs identical modulation affecting each server independently.

Keywords

Status: accepted

Back to the list of papers