Title: Busy period of a single-server Poisson queueing system with splitting and batch delayed-feedback

Authors: Aliakbar Montazer Haghighi; Dimitar P. Mishev

Addresses: Department of Mathematics, Prairie View A&M University, P.O. Box 519 – MS2225, Prairie View, Texas 77446 0519, USA ' Department of Mathematics, Prairie View A&M University, P.O. Box 519 – MS2225, Prairie View, Texas 77446 0519, USA

Abstract: We consider a queueing system consisting of a service station, a splitter and a delay station. There are two types of arrivals to the service station. External tasks arrive according to a Poisson process while internal tasks arrive as batches from the delay station, also according to a Poisson process but with a different parameter. There is a single server at the service station and a processor at the delay station. Splitting is immediate. Each of the two stations has a buffer as its waiting room. The service distribution is exponential. Feedbacks occur exponentially with delay and in batches of certain sizes. We consider the busy period of the server and an algorithm for computing the expected number of busy periods in the service station, which is of Takács's renewal equation form. Some numerical examples are also offered.

Keywords: busy periods; batch delayed feedback; splitting; single-server Poisson queueing; service stations; queues; delay stations.

DOI: 10.1504/IJMOR.2016.074859

International Journal of Mathematics in Operational Research, 2016 Vol.8 No.2, pp.239 - 257

Received: 29 Mar 2014
Accepted: 11 Aug 2014
Published online: 21 Feb 2016 *

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