Analysis of the queue-length distribution for the discrete-time batch-service Geo/Ga,Y/1/K queue

Yi, Xeung W.; Kim, Nam Kyu; Yoon, Bong K.; Chae, Kyung-Chul

doi:10.1016/j.ejor.2006.08.016

Cited by 26 publications

(10 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In most of the papers (Arumuganathan and Yi et al 2007), expressions are obtained for the distribution of the number of customers in the system at various time epochs and for several service policies (the service policy establishes when an available server is allowed to start processing). The customer delay, however, has attracted less attention, for instance in Chaudhry and Templeton 1983;Cohen 1969;Dagsvik 1975;Downton 1955;Keilson 1962; Kim and Chaudhry 2006;Medhi 1975;Miller 1959.…”

mentioning

confidence: 99%

Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service

et al. 2009

View full text Add to dashboard Cite

Whereas the buffer content of batch-service queueing systems has been studied extensively, the customer delay has only occasionally been studied. The few papers concerning the customer delay share the common feature that only the moments are calculated explicitly. In addition, none of these surveys consider models including the combination of batch arrivals and a server operating under the full-batch service policy (the server waits to initiate service until he can serve at full capacity). In this paper, we aim for a complete characterisation -i.e., moments and tail probabilities -of the customer delay in a discrete-time queueing system with batch arrivals and a batch server adopting the full-batch service policy. In addition, we demonstrate that the distribution of the number of customer arrivals in an arbitrary slot has a significant impact on the moments and the tail probabilities of the customer delay.

show abstract

mentioning

confidence: 99%

Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service

et al. 2009

View full text Add to dashboard Cite

show abstract

“…Batch-service queueing models have been studied extensively during the past decades [2], [6]- [9], [11]- [12], [16]- [17], [19], [21], [24], [26], [28]- [29], [31]. However, these surveys share the common feature that only models with an uncorrelated arrival process are considered, which is unrealistic in several real-life situations.…”

Section: Introductionmentioning

confidence: 99%

A Batch-Service Queueing Model with a Discrete Batch Markovian Arrival Process

Claeys

Walraevens

Laevens

et al. 2010

Analytical and Stochastic Modeling Techniques and Applications

View full text Add to dashboard Cite

Abstract. Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of customers in system (system content) reaches or exceeds a threshold. Correlation is taken into account by assuming a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. We deduce the probability generating function of the system content at random slot marks and we examine the influence of correlation in the arrival process on the behavior of the system. We show that correlation merely has a small impact on the threshold that minimizes the mean system content. In addition, we demonstrate that correlation might have a significant influence on the system content and therefore has to be included in the model.

show abstract

“…However, the focus was mainly put on the number of waiting customers (see e.g. [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]), whereas the waiting time of customers, also called customer delay, has attracted very few attention, especially in the case of batch arrivals. In [17], [18] and [19] we have computed the probability generating function (PGF) of the customer delay in distinct discrete-time queueing models with batch arrivals and batch service.…”

Section: Introductionmentioning

confidence: 99%

Tail probabilities of the delay in a batch-service queueing model with batch-size dependent service times and a timer mechanism

Claeys

Steyaert

Walraevens

et al. 2013

Computers & Operations Research

View full text Add to dashboard Cite

We deduce approximations for the tail probabilities of the customer delay in a discrete-time queueing model with batch arrivals and batch service. As in telecommunications systems transmission times are dependent on packet sizes, we consider a general dependency between the service time of a batch and the number of customers within it. The model also incorporates a timer mechanism to avoid excessive delays stemming from the requirement that a service can only be initiated when the number of present customers reaches or exceeds a service threshold. The service discipline is first-come, first-served (FCFS). We demonstrate in detail that our approximations are very useful for the purpose of assessing the order of magnitude of the tail probabilities of the customer delay, except in some special cases that we discuss extensively. We also illustrate that neglecting batch-size dependent service times or a timer mechanism can lead to a devastating assessment of the tail probabilities of the customer delay, which highlights the necessity to include these features in the model. The results from this paper can, for instance, be applied to assess the quality of service (QoS) of Voice over IP (VoIP) conversations, which is typically expressed in terms of the order of magnitude of the probability of Computers & Operations Research May 1, 2013 packet loss due to excessive delays. Preprint submitted to

show abstract

Analysis of the queue-length distribution for the discrete-time batch-service Geo/Ga,Y/1/K queue

Cited by 26 publications

References 6 publications

Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service

Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service

A Batch-Service Queueing Model with a Discrete Batch Markovian Arrival Process

Tail probabilities of the delay in a batch-service queueing model with batch-size dependent service times and a timer mechanism

Contact Info

Product

Resources

About