Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals
In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characteri...
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doaj-d59e70f62dfc4f9f89e172e177d71a962021-07-23T13:52:42ZengMDPI AGMathematics2227-73902021-07-0191709170910.3390/math9141709Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and ArrivalsFreek Verdonck0Herwig Bruneel1Sabine Wittevrongel2SMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, 9000 Gent, BelgiumSMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, 9000 Gent, BelgiumSMACS Research Group, Department of Telecommunications and Information Processing (TELIN), Ghent University (UGent), Sint-Pietersnieuwstraat 41, 9000 Gent, BelgiumIn this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characterized by its own distributions for the number of arrivals and the number of available servers in a slot. Within a state, these numbers are independent and identically distributed random variables. State changes can only occur at slot boundaries and mark the beginnings and ends of state periods. Each state has its own distribution for its period lengths, expressed in the number of slots. The stochastic process that describes the state changes introduces correlation to the system, e.g., long periods with low arrival intensity can be alternated by short periods with high arrival intensity. Using probability generating functions and the theory of the dominant singularity, we find the tail probabilities of the delay.https://www.mdpi.com/2227-7390/9/14/1709queueing theorydiscrete-timemultiservercorrelationdelaytail |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Freek Verdonck Herwig Bruneel Sabine Wittevrongel |
spellingShingle |
Freek Verdonck Herwig Bruneel Sabine Wittevrongel Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals Mathematics queueing theory discrete-time multiserver correlation delay tail |
author_facet |
Freek Verdonck Herwig Bruneel Sabine Wittevrongel |
author_sort |
Freek Verdonck |
title |
Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals |
title_short |
Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals |
title_full |
Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals |
title_fullStr |
Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals |
title_full_unstemmed |
Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals |
title_sort |
delay in a 2-state discrete-time queue with stochastic state-period lengths and state-dependent server availability and arrivals |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2021-07-01 |
description |
In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characterized by its own distributions for the number of arrivals and the number of available servers in a slot. Within a state, these numbers are independent and identically distributed random variables. State changes can only occur at slot boundaries and mark the beginnings and ends of state periods. Each state has its own distribution for its period lengths, expressed in the number of slots. The stochastic process that describes the state changes introduces correlation to the system, e.g., long periods with low arrival intensity can be alternated by short periods with high arrival intensity. Using probability generating functions and the theory of the dominant singularity, we find the tail probabilities of the delay. |
topic |
queueing theory discrete-time multiserver correlation delay tail |
url |
https://www.mdpi.com/2227-7390/9/14/1709 |
work_keys_str_mv |
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