The complete analysis of the discrete time finite DBMAP/G/1/N queue

Herrmann, Christoph

doi:10.1016/s0166-5316(00)00037-7

Cited by 34 publications

(22 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Taking the second-order derivative of (25) and applying the rule of de l'Hospital to the term for p = 0, we have…”

Section: Mean Value and Variance Of The Delaymentioning

confidence: 99%

“…Considering the fact that the x p 's are the roots of the equation 1 − zx c = 0, the pgf of the packet delay can be simplified from (25) and (26) as…”

Section: Tail Probabilities Of the Delaymentioning

confidence: 99%

“…We mention [18], where the service times are assumed to be geometrically distributed; somewhat related models with randomly interrupted servers are studied in [19] and [20]. Geometric service times are also considered in [21] and [22], while [23]- [25] deal with general service times, but only for the case of one single server.…”

Section: Introductionmentioning

confidence: 99%

“…In order to find the dominant pole z d , note that from (2), (25) and (26), it follows that poles of D(z) are to be found among the following z's:…”

mentioning

confidence: 99%

See 3 more Smart Citations

Discrete-time multiserver queues with geometric service times

Gao

Wittevrongel

Bruneel

2004

Computers & Operations Research

View full text Add to dashboard Cite

Scope and purposeDiscrete-time queueing models are widely used to study the behavior of various types of telecommunication and computer systems. Most of the existing studies of discrete-time multiserver queueing models assume that the service times of the customers are constant.Recently, however, there has been an increased interest in discrete-time models with nondeterministic service times, due to the more and more complicated and irregular service mechanisms in nowadays telecommunication networks. In view of this, this paper focuses on a discrete-time queueing system with multiple servers and geometrically distributed service In this paper, a discrete-time multiserver queueing system with infinite buffer size and general independent arrivals is considered. The service times of a packet served by one of the servers are assumed to be independent and identically distributed according to a geometric distribution. Each packet gets service from only one server. In the paper, the behavior of the queueing system is studied analytically by means of a generating-functions approach.This results in closed-form expressions for the mean values, the variances and the tail distributions of the system contents and the packet delay. Some numerical examples are given to illustrate the analysis.

show abstract

“…Taking the second-order derivative of (25) and applying the rule of de l'Hospital to the term for p = 0, we have…”

Section: Mean Value and Variance Of The Delaymentioning

confidence: 99%

“…Considering the fact that the x p 's are the roots of the equation 1 − zx c = 0, the pgf of the packet delay can be simplified from (25) and (26) as…”

Section: Tail Probabilities Of the Delaymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In order to find the dominant pole z d , note that from (2), (25) and (26), it follows that poles of D(z) are to be found among the following z's:…”

mentioning

confidence: 99%

See 2 more Smart Citations

Discrete-time multiserver queues with geometric service times

Gao

Wittevrongel

Bruneel

2004

Computers & Operations Research

View full text Add to dashboard Cite

show abstract

“…Shown in Ref. [17], the matrix-form generating function of P ½d ðw; lÞ; i.e. P ½d p ðz; lÞ ¼ P 1 w¼0 P ½d ðw; lÞz w has the following form:…”

Section: N¼0mentioning

confidence: 99%

Traffic splitting in a network: split traffic models and applications

Ferng

2004

Computer Communications

View full text Add to dashboard Cite

The contemporary high-speed networks, e.g. the Internet and asynchronous transfer mode (ATM) networks provide a convenient and cost-effective communication platform to carry the emerging multimedia applications. However, problems, such as network congestion caused by overloaded traffic get worse day by day. Thus, how to properly control the system while maintaining the quality of service (QoS) for users becomes an important and challenging issue. To reach the goal of QoS guarantee, load sharing or traffic balancing is one of important techniques to improve the whole network performance. In this paper, we focus on the probabilistic routing policy and analyze split traffic models under such a probabilistic routing policy with input traffic models of the batch Markovian arrival process (BMAP) and discrete-time BMAP (D-BMAP) which can be employed to characterize the multimedia traffic in current and future networks. We successfully show that the split traffic on each routing path from an original BMAP (D-BMAP) input is still a BMAP (D-BMAP). The detailed traffic structure is also acquired. Applying traffic splitting along with the output process characterization, we propose a network-wise performance evaluation method suitable for mesh networks with a probabilistic routing algorithm to get the end-to-end delay, delay variance, and cell loss probability. With numerical experiments, we show that (i) the probabilistic routing policy with a random routing matrix performs well for systems; (ii) the proposed method of network-wise performance analysis has good accuracy. q

show abstract

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

The complete analysis of the discrete time finite DBMAP/G/1/N queue

Cited by 34 publications

References 12 publications

Discrete-time multiserver queues with geometric service times

Discrete-time multiserver queues with geometric service times

Traffic splitting in a network: split traffic models and applications

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

Contact Info

Product

Resources

About