Spectral Expansion Solution Methodology for QBD-M Processes and Applications in Future Internet Engineering

Do, Tien Van; Chakka, Ram; Sztrik, János

doi:10.1007/978-3-319-00293-4_11

Cited by 8 publications

(3 citation statements)

References 31 publications

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“…As a result, its values are critical for the success of any application. A general communication system consists of the network interconnection [1][2][3] with notes where the packets are serviced. In order to perform parallel computations, the processors have to compute the packets along several communication lines [4].…”

Section: Introductionmentioning

confidence: 99%

A Model for Compound Poisson Process Queuing System with Batch Arrivals and Services

Saritha¹,

Mamatha²,

Reddy³

et al. 2020

JESA

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Computing and logistics management systems have a wide area of applications with compound Poisson process Markov system with a batch servicing facility where customers arrive either independently or batches for service into the multi-server queues. The service of the customers is processed either independently or batch-wise based on the requirement of various sizes. The order of service has been found to follow First Come First Service while customers arrive according to the exponential distribution. A mathematical model is proposed to process customers by using generalized spectral expansion method. The explicit type required to service the system is measured as buffer size. For accurate assessment of performance, numerical results have been depicted in graphical form. Keywords:mean queue length, batch arrivals and batch services, QBD -M, multi-server system, compound poisson process THE STEADY-STATE ANALYSIS AND QBD -M PROCESS WITH MULTIPLE JUMPSThe multiprocessor system is modeled by generalized finite QBD -M (Quasi Birth and Death) process with multiple boundaries. Here, the parameter M refers to multiple jumps in the level dimension. A novel approach theory has been evaluated for the steady-state analysis of the system. Unlike

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Section: Introductionmentioning

confidence: 99%

A Model for Compound Poisson Process Queuing System with Batch Arrivals and Services

Saritha¹,

Mamatha²,

Reddy³

et al. 2020

JESA

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“…We developed an effective method for the calculation of state probabilities of the large dimension 3-D MC. There is much research on solving similar problems for the large dimension 2-D MC [9][10][11][12][13][14][15][16][17][18][19][20]. However, almost all of them have similar problems related to ill-conditioned matrices which arise during computational procedures.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Space Merging Algorithm for Analysis of Two Stage Queueing Network with Feedback

Melikov¹,

Пономаренко

Rustamov

et al. 2016

Communications in Computer and Information Science

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Abstract. A Markov model of two stage queuing network with feedback is proposed. Poisson flows arriving to both stages from outside and part of already serviced calls in the first node instantaneously enter to the second node (if there is free space here) while the remaining part leaves the network. At the completion of call processing in the second node there are three possibilities: (1) it leaves the network; (2) it instantaneously feeds back to the first node (if there is free space here); (3) it feeds back to the first node after some delay in orbit. All feedbacks are determined by known probabilities. Both nodes have finite capacities. The mathematical model of the investigated network is a three dimensional Markov chain (3-D MC) and hierarchical space merging algorithm to calculate its steady-state probabilities is developed. This algorithm allows asymptotic analysis of the quality of service (QoS) metrics of the investigated network as well.

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“…The current state of mathematical theory of the teletraffic problems has been collected in a detailed review [1]. That paper and other ones justify that performance evaluation of wireless networks plays a central role, see for example [2], [4], [5], [8], [13]. Developing effective methods to calculate QoS metrics of integrated cellular networks under various Call Admission Control (CAC) schemes are important, see [10], [12].…”

Section: Introductionmentioning

confidence: 99%

Performance Evaluation of Integrated Wireless Networks with Virtual Partition of Channels

Melikov

Fattakhova

Velidzanova

et al. 2014

Communications in Computer and Information Science

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Abstract.A new access scheme in integrated wireless networks which is based on virtual partition of channels among voice and data calls is proposed. In this scheme a voice call occupies a free channel in its own zone and if there is no available channel in the given zone a handover voice call searches for an idle channel in another zone. A threshold for number of handover voice calls in zone of channels for data calls is defined. To determine the access scheme of new data calls a state-dependent threshold based rule is introduced. An effective method to calculate the QoS metrics of the defined access scheme is developed. Some sample results illustrating the numerical experiments are collected and analyzed.

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Spectral Expansion Solution Methodology for QBD-M Processes and Applications in Future Internet Engineering

Cited by 8 publications

References 31 publications

A Model for Compound Poisson Process Queuing System with Batch Arrivals and Services

A Model for Compound Poisson Process Queuing System with Batch Arrivals and Services

Hierarchical Space Merging Algorithm for Analysis of Two Stage Queueing Network with Feedback

Performance Evaluation of Integrated Wireless Networks with Virtual Partition of Channels

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