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A Discrete-Time Retrial Queueing Model With One Server
R.D. Nobel
- pp 3-15
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TLDR
In this article, a one-server queueing model with retrials in discrete-time is presented, where the number of primary jobs arriving in a time slot follows a general probability distribution and the different numbers of primary arrivals in consecutive time slots are mutually independent.Abstract:
This paper presents a one-server queueing model with retrials in discrete-time. The number of primary jobs arriving in a time slot follows a general probability distribution and the different numbers of primary arrivals in consecutive time slots are mutually independent. Each job requires from the server a generally distributed number of slots for its service, and the service times of the different jobs are independent. Jobs arriving in a slot can start their service only at the beginning of the next slot. When upon arrival jobs find the server busy all incoming jobs are sent into orbit. When upon arrival in a slot jobs find the server idle, then one of the incoming jobs (randomly chosen) in that slot starts its service at the beginning of the next slot, whereas the other incoming jobs in that slot, if any, are sent into orbit. During each slot jobs in the orbit try to re-enter the system individually, independent of each other, with a given retrial probability. The ergodicity condition and the generating function of the joint equilibrium distribution of the number of jobs in orbit and the residual service time of the job in service are calculated. From the generating function several performance measures are deduced, like the average orbit size. Also the busy period and the number of jobs served during a busy period are discussed. To conclude, extensive numerical results are presented.read more
Citations
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Journal ArticleDOI
A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH SERVER BREAKDOWNS
Ivan Atencia,Pilar Moreno +1 more
TL;DR: A stochastic decomposition law is derived from the Markov chain underlying the considered queueing system and the concept of generalized service time is introduced and a recursive procedure is developed to obtain the steady-state distributions of the orbit and system size.
Journal ArticleDOI
A Geo/G/1 retrial queueing system with priority services
TL;DR: It is proved that the M/G/1 retrial queue with service interruptions can be approximated by the corresponding discrete-time system, and the stochastic decomposition law has been derived and bounds for the proximity between the steady-state distributions for the considered queueing system and its corresponding standard system are obtained.
Journal ArticleDOI
Retrial queueing models in discrete time: a short survey of some late arrival models
TL;DR: This paper presents an overview of one-server queueing models with retrials in discrete-time, and only models with delayed access are considered, and the so-called late arrival setup is chosen.
Journal ArticleDOI
A Discrete-Time Unreliable Geo/G/1 Retrial Queue with Balking Customers, Second Optional Service, and General Retrial Times
Feng Zhang,Zhifeng Zhu +1 more
TL;DR: In this article, the steady-state behavior of a discrete-time unreliable Geo/G/1 retrial queueing system with balking customers and second optional service is investigated.
Proceedings ArticleDOI
A discrete-time queueing model with abandonments
R.D. Nobel,Suzanne van der Ster +1 more
TL;DR: This paper presents a multi-server queueing model with abandonments in discrete time, in which each customer waiting in the queue decides to abandon the system forever with a fixed (abandon) probability.
References
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Book
Discrete-time models for communication systems including ATM
Herwig Bruneel,B.G. Kim +1 more
TL;DR: This chapter discusses Discrete-Time Models and Applications, Applications to ATM, and more, which describes the development of the GI-G-1 Model and its applications.
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TL;DR: Stochastic Processes Queueing Systems: general concepts birth-and-death queuing systems: Exponential models non-birth-anddeath queueing systems: Markovian models network of queues Non-Markovian Queue-based systems with general Arrival Time and Service Time Distributions 333 Miscellaneous Topics as mentioned in this paper
Journal ArticleDOI
Discrete-Time Queuing Theory
TL;DR: In this paper, a single-server queuing system for which time is treated as a discrete variable is analyzed, where the number of customers arriving within a fixed time interval is assumed to obey a binomial probability distribution.