A batch-service queueing model with a discrete batch Markovian arrival process

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

Forgalom modellezési módszerek fejlesztése = Advanced traffic modeling techniques

A projekt alapvetően sikeresen járult hozzá a vizsgált szakterület eredményeinek bővítéséhez és a résztvevő kutatócsoport fejlődéséhez. A projekt eredményihez kapcsolódó dolgozatok alapján PHD fokozatot szerzett Bodrog Levente és Saffer Zsolt. A projekt eredményeit összegző publikációk együttes impakt faktora ~22. A szakmai eredmenyek közül Markov érkezési folyamatok alapvető tulajdonságait összegző cikk (A minimal representation of Markov arrival processes and a moments matching method) emelhető ki, amelyik időközben az ezen folyamatok illesztési korlátait vizsgálló munkák alapjává vált. | The project successfully enhanced the field of traffic modeling of computer and communication systems and helped to improve the carrier of the involved research group. Based on the their theses summarizing parts of the results of the project Bodrog Levente and Saffer Zsolt were awarded the doctor of philosophy degree. The cumulated impact factor of the journal papers publish the research results of the project is about 22. The most remarkable research results are in the paper summarizing some basic properties of Markov arrival processes (A minimal representation of Markov arrival processes and a moments matching method), which become a basic reference for subsequent works dealing with the fitting properties of these processes

Analysis of a multi-server queueing model with vacations and optional secondary services

In this paper we study a multi-server queueing model in which the customer arrive according to a Markovian arrival process. The customers may require, with a certain probability, an optional secondary service upon completion of a primary service. The secondary services are offered (in batches of varying size) when any of the following conditions holds good: (a) upon completion of a service a free server finds no primary customer waiting in the queue and there is at least one secondary customer (including possibly the primary customer becoming a secondary customer) waiting for service; (b) upon completion of a primary service, the customer requires a secondary service and at that time the number of customers needing a secondary service hits a pre-determined threshold value; (c) a server returning from a vacation finds no primary customer but at least one secondary customer waiting. The servers take vacation when there are no customers (either primary or secondary) waiting to receive service. The model is studied as a QBD-process using matrix-analytic methods and some illustrative examples arediscussed

Performance of the sleep-mode mechanism of the new IEEE 802.16m proposal for correlated downlink traffic

There is a considerable interest nowadays in making wireless telecommunication more energy-efficient. The sleep-mode mechanism in WiMAX (IEEE 802.16e) is one of such energy saving measures. Recently, Samsung proposed some modifications on the sleep-mode mechanism, scheduled to appear in the forthcoming IEEE 802.16m standard, aimed at minimizing the signaling overhead. In this work, we present a performance analysis of this proposal and clarify the differences with the standard mechanism included in IEEE 802.16e. We also propose some special algorithms aimed at reducing the computational complexity of the analysis

Markovian arrivals in stochastic modelling: a survey and some new results

This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, nonhomogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension.Peer Reviewe

Findings about the two-state BMMPP for modeling point processes in reliability and queueing systems

The Batch Markov Modulated Poisson Process (BMMPP) is a subclass of the versatile Batch Markovian Arrival process (BMAP) which have been widely used for the modeling of dependent and correlated simultaneous events (as arrivals, failures or risk events, real-time multimedia communications). Both theoretical and applied aspects are examined in this paper. On one hand, the identifiability of the stationary BMMPP2(K) is proven, where K is the maximum batch size. This is a powerful result when inferential tasks related to real data sets are carried out. On the other hand, some findings concerning the correlation and autocorrelation structures are provided.The first and second authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, research project ECO2015-66593-P. The Third author acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, research project MTM2015-65915-R; and also from Junta de Andalucía, and BBVA Fundation, research project P11- FQM-7603 and FQM-32

Performance of the IEEE 802.16e sleep mode mechanism in the presence of bidirectional traffic

We refine existing performance studies of the WiMAX sleep mode operation to take into account uplink as well as downlink traffic. This as opposed to previous studies which neglected the influence of uplink traffic. We obtain numerically efficient procedures to compute both delay and energy efficiency characteristics. A test scenario with an Individual Subscriber Internet traffic model in both directions shows that even a small amount of uplink traffic has a profound effect on the system performance