Tail distribution of the delay in a general batch-service queueing model

Claeys, Dieter; Steyaert, Bart; Walraevens, Joris; Laevens, Koenraad; Bruneel, Herwig

doi:10.1016/j.cor.2012.02.004

Cited by 11 publications

(17 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper, we extend our previous work [22]. In [22], the service times do not depend on the batch sizes, whereas in actual telecommunications systems transmission times depend on packet sizes. In addition, it has been shown in [22] that in case of light traffic, the delay can be extremely high when a minimum batch size is enforced.…”

Section: Introductionmentioning

confidence: 48%

“…The postponing delay would then represent the time, starting at the same moment as the queueing delay, until the batch containing the tagged customer contains at least l customers or until the timer has expired. As a result, similar approximations as in [22] would be obtained: the lower bound…”

Section: Deduction Of Approximation Formulasmentioning

confidence: 96%

“…It can thus be expressed as an integral number of slots. In [22] for a system without timer mechanism, we have decomposed the delay W of a randomly tagged customer as the maximum of two parts:…”

Section: Deduction Of Approximation Formulasmentioning

confidence: 99%

“…In [22], the service times do not depend on the batch sizes, whereas in actual telecommunications systems transmission times depend on packet sizes. In addition, it has been shown in [22] that in case of light traffic, the delay can be extremely high when a minimum batch size is enforced. Therefore, in the model studied in this paper, we consider a general dependency between the service time of a batch and the number of customers within it, and we include a timer mechanism that avoids excessive delays in case of light traffic as well.…”

Section: Introductionmentioning

confidence: 99%

“…In [22], we have considered a more versatile model with a minimum batch size (also called service threshold) l (i.e., service is initiated only if at least l customers are present, with l some value between 1 and the server capacity) and generally distributed service times. In this paper, we extend our previous work [22]. In [22], the service times do not depend on the batch sizes, whereas in actual telecommunications systems transmission times depend on packet sizes.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Self Cite

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

Section: Introductionmentioning

confidence: 48%

Section: Deduction Of Approximation Formulasmentioning

confidence: 96%

Section: Deduction Of Approximation Formulasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Self Cite

View full text Add to dashboard Cite

show abstract

System Occupancy of a Two-Class Batch-Service Queue with Class-Dependent Variable Server Capacity

Baetens

Steyaert

Claeys

et al. 2016

Analytical and Stochastic Modelling Techniques and Applications

Self Cite

View full text Add to dashboard Cite

Abstract. Due to their wide area of applications, queueing models with batch service, where the server can process several customers simultaneously, have been studied frequently. An important characteristic of such batch-service systems is the size of a batch, that is the number of customers that are processed simultaneously. In this paper, we analyse a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common first-come-first served single-server queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the number of consecutive same-class customers. After establishing the system equations that govern the system behaviour, we deduce an expression for the steady-state probability generating function of the system occupancy at random slot boundaries. Also, some numerical examples are given that provide further insight in the impact of the different parameters on the system performance.

show abstract

Delay analysis of a two-class batch-service queue with class-dependent variable server capacity

et al. 2018

Self Cite

View full text Add to dashboard Cite

In this paper, we analyse the delay of a random customer in a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common single-server first-come-first-served queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the length of a sequence of same-class customers. This type of batch server can be found in telecommunications systems and production environments. We first determine the steady state partial probability generating function of the queue occupancy at customer arrival epochs. Using a spectral decomposition technique, we obtain the steady state probability generating function of the delay of a random customer. We also show that the distribution of the delay of a random customer corresponds to a phase-type distribution. Finally, some numerical examples are given that provide further insight in the impact of asymmetry and variance in the arrival process on the number of customers in the system and the delay of a random customer.

show abstract

Tail distribution of the delay in a general batch-service queueing model

Cited by 11 publications

References 35 publications

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

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

System Occupancy of a Two-Class Batch-Service Queue with Class-Dependent Variable Server Capacity

Delay analysis of a two-class batch-service queue with class-dependent variable server capacity

Contact Info

Product

Resources

About