TY - GEN

T1 - A Discrete-Time Queueing Model in a Random Environment

AU - Nobel, Rein

AU - Rondaij, Annette

PY - 2019

Y1 - 2019

N2 - To study the effect of burstiness in arrival streams on the congestion in queueing systems this paper presents a one-server queueing model in a random environment in discrete time. The environment can be in two states. The number of time slots between two consecutive transitions of the environment follows a geometric distribution with a transition-dependent parameter. In every slot customers arrive in batches, and the batch-size distribution depends on the environment. Each customer requires a generally distributed service time. Arriving customers are put in a queue which is served in FIFO order. Arrivals have precedence over departures and departures have precedence over a change of the environment. The generating functions of the number of customers in the queue and the individual waiting time will be derived. Numerical results will show the effect of the burstiness in the arrival stream on the waiting-time and the queue-size distribution by calculating in parallel the corresponding results for the standard discrete-time model with a mixed batch-size distribution, ceteris paribus.

AB - To study the effect of burstiness in arrival streams on the congestion in queueing systems this paper presents a one-server queueing model in a random environment in discrete time. The environment can be in two states. The number of time slots between two consecutive transitions of the environment follows a geometric distribution with a transition-dependent parameter. In every slot customers arrive in batches, and the batch-size distribution depends on the environment. Each customer requires a generally distributed service time. Arriving customers are put in a queue which is served in FIFO order. Arrivals have precedence over departures and departures have precedence over a change of the environment. The generating functions of the number of customers in the queue and the individual waiting time will be derived. Numerical results will show the effect of the burstiness in the arrival stream on the waiting-time and the queue-size distribution by calculating in parallel the corresponding results for the standard discrete-time model with a mixed batch-size distribution, ceteris paribus.

KW - Discrete-time queue

KW - Generating functions

KW - Random environment

UR - http://www.scopus.com/inward/record.url?scp=85077126302&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85077126302&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-27181-7_20

DO - 10.1007/978-3-030-27181-7_20

M3 - Conference contribution

AN - SCOPUS:85077126302

SN - 9783030271800

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 330

EP - 348

BT - Queueing Theory and Network Applications

A2 - Phung-Duc, Tuan

A2 - Kasahara, Shoji

A2 - Wittevrongel, Sabine

PB - Springer

T2 - 14th International Conference on Queueing Theory and Network Applications, QTNA 2019

Y2 - 27 August 2019 through 29 August 2019

ER -