A Case Study of Multiserver ATM Buffers Routing Multimedia Traffics with Geometric Service Time

Nada, Fayza A.

doi:10.1109/iccee.2009.162

Cited by 5 publications

(9 citation statements)

References 6 publications

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“…where s = 1 − s and A(x, y) is defined as the joint PGF of the total size of the batch that arrives into the system in slot k. A solution to (26) has been described in [48], but with a small mistake (without some brackets in the denominator). Note that hypotheses (A) and (B) are valid.…”

Section: Fe 20: Multiserver Atm Buffers Routing Multimedia Trafficsmentioning

confidence: 99%

“…The following equation arises [48] from a two dimensional Geo A1+A2 /Geo/c traffic model, which means batch arrival of two classes of packets with size A 1 of class 1 packets and size A 2 of class 2 packets, geometric distribution to the inter-arrival time, geometric service time, and c servers. A special case has been considered, illustrated in Fig.…”

Section: Fe 20: Multiserver Atm Buffers Routing Multimedia Trafficsmentioning

confidence: 99%

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On the structure and solutions of functional equations arising from queueing models

2017

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Abstract. It is a survey on functional equations of a certain type, for functions in two complex variables, which often arise in queueing models. They share a common pattern despite their apparently different forms. In particular, they invariably characterize the probability generating function of the bivariate distribution characterizing a two-queue system and their forms depend on the composition of the underlying system. Unfortunately, there is no general methodology of solving them, but rather various ad-hoc techniques depending on the nature of a particular equation; most of the techniques involve advanced complex analysis tools. Also, the known solutions to particular cases of this type of equations are in general of quite involved forms and therefore it is very difficult to apply them practically. So, it is clear that the issues connected with finding useful descriptions of solutions to these equations create a huge area of research with numerous open problems. The aim of this article is to stimulate a methodical study of this area. To this end we provide a survey of the queueing literature with such two-place functional equations. We also present several observations obtained while preparing it. We hope that in this way we will make it easier to take some steps forward on the road towards a (more or less) general solving theory for this interesting class of equations.Mathematics Subject Classification. 05A15, 30D05, 30E25, 39B32, 60K25, 65Q20.

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Section: Fe 20: Multiserver Atm Buffers Routing Multimedia Trafficsmentioning

confidence: 99%

Section: Fe 20: Multiserver Atm Buffers Routing Multimedia Trafficsmentioning

confidence: 99%

On the structure and solutions of functional equations arising from queueing models

2017

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“…Several models have been used to describe the interruption process. While both analytical and numerical results have been obtained on many occasions with respect to performance measures related to the buffer contents distribution [4], [3] for the case of multiserver [5], [6] as well as for the single server case [7] the derivation of delay characteristics has received much less attention in the past. More specifically, analytic results have been limited primarily to the single server case, whereas the multiple server case has mainly been investigated by means of numerical methods.…”

Section: Introductionmentioning

confidence: 99%

“…Usually, the quantities studied in these investigations are the buffer occupancy, system occupancy, and the delays (waiting times) experienced by the packets in the buffer [1], [2]. In [8], [9] the delays in various multiserver systems are investigated, and in [3] packet delays in single server systems with various types of first order Markovian correlated arrival processes are studied. Also, the discrete-time queues with or without server interruptions have received great attention in the scientific literature.…”

Section: Introductionmentioning

confidence: 99%

Analyzing buffer contents of space division output buffered multichannel switches

Nada¹

2014

Communications on Advanced Computational Science with Applicati

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In digital communication systems, buffers are used for the temporary storage of digital information awaiting transmission via some communication channel(s). In this article, buffer analysis of space division output buffered switches operating in an ATM environment is presented. The switch is modeled as a discrete-time, batch arrival, multiserver queuing system, with infinite buffer and geometric service time. Probability Generating Functions (PGFs) of the system occupancy are derived for single server, two servers, and a general form for multiserver systems. Expectations for the corresponding random variables are obtained for different cases. Many numerical examples, which verify the results, are presented.

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“…In [9], [10], [11] the delays in various multiserver systems are investigated, and in [12] packet delays in single server systems with various types of first order Markovian correlated arrival processes are studied. Also, the discretetime queues with or without server interruptions have received great attention in the scientific literature.…”

Section: Introductionmentioning

confidence: 99%

Performance Evaluation of Space Division Output Buffered Switches

Nada

Rakha²

2015

Automatika

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Original scientific paperDiscrete-time multiserver queues have been successfully used in the performance evaluation of computer and communication systems in various contexts such as TDM, voice-data integration, deflection routing and more recently, ATM-switching technology. In digital communication systems, buffers are used for the temporary storage of digital information awaiting transmission via some communication channel(s). Usually, information presents itself in the form of fixed-size packets, and synchronous (slotted) transmission is used so that the buffers can be modelled as discrete-time queuing systems. In this article, performance analysis of space division output buffered switches operating in an ATM multimedia environment is presented. Fixed size packets arrive onto the switch inputs in each time slot. The switch is modelled as a discrete-time, batch arrival, multiserver queuing system, with infinite buffer and geometric service times. The main contribution of this work is using multiserver case and geometric service time. Many performance measures such as System occupancy, Queuing time, Unfinished work and Waiting time are analysed. Probability Generating Functions (PGFs) and expectations for the corresponding random variables are derived. The results of the analysis have been verified in many ways. First, they have been used to generate the results of some previous analyses as special cases. Second, they obviously seem to preserve classical queuing relations (e.g. the famous Little's formula). Last, they have been shown to generate intuitively acceptable graphs, when translated into numerical values.Key words: Data Communications, Performance Analysis, Output Buffered Switches, System Occupancy, Multiserver queues Procjena učinkovitosti prospajanja komutatora. Diskretni višeserverski redovi uspješno su korišteni kod analize učinkovitosti računalnih i komunikacijskih sustava u različitim okolnostima poput TDM-a, glasovnopodatkovne integracije, ATM komutatora. U sustavima digitalnih komunikacija bufferi se koriste za privremeno pohranjivanje digitalnih informacija koječekaju na prijenos preko komunikacijskih kanala. Uobičajeno se informacije prikazuju u formi paketa fiksne veličine, a sinkronizirani prijenos koristi se kako bi bufferi mogli biti modelirani kao diskretni sustav sčekanjem. U ovomečlanku prikazana je analiza učinkovitosti komutatora u ATM multimedijskom okruženju. Paketi fiksne veličine stižu na ulaze preklopnika u svakom vremenskom okviru. Preklopnik je modeliran kao diskretni višeserverski sustav s batch dolascima, s beskonačnim bufferom i geometrijskom razdiobom vremena servisa. Glavni doprinos ovog rada je korištenje višeserverskog slučaja i geometrijske razdiobe vremena servisa. Analizirane su mnoge mjere učinkovitosti kao što je zauzetost sustava, vrijemečekanja, nezavršen posao. Izvedena je funkcija izvodnica i očekivanje za odgovarajuće slučajne varijable. Rezultati analize provjereni su na mnoge načine. Prvo su korišteni za generiranje rezultata nekih prethodnih analiza kao po...

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A Case Study of Multiserver ATM Buffers Routing Multimedia Traffics with Geometric Service Time

Cited by 5 publications

References 6 publications

On the structure and solutions of functional equations arising from queueing models

On the structure and solutions of functional equations arising from queueing models

Analyzing buffer contents of space division output buffered multichannel switches

Performance Evaluation of Space Division Output Buffered Switches

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