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finite-buffer Bulk Service Queue Under Markovian Service Process: GI/MSP(a,b)/1/N

STOCHASTIC ANALYSIS AND APPLICATIONS 2009年第3期27卷 500-522页

作者： Banik, A. D. Gupta, U. C. Chaudhry, M. L. Tata Inst Fundamental Res Sch Technol & Comp Sci Bombay 400005 Maharashtra India Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India Royal Mil Coll Canada Dept Math & Comp Sci Kingston ON K7K 5L0 Canada

We consider a single-server queue with renewal input and Markovian service process where server serves customers in batches according to a general bulk service rule. Queue length distributions at pre-arrival and arbitrary epochs have been obtained along with some important performance measures such as probability of blocking, mean queue lengths and mean waiting times. The analysis has been carried out assuming finite-buffer space for the arriving customers. The model has potential applications in areas such as computer networks, telecommunication systems and manufacturing systems.

关键词： finite-buffer General bulk service rule General independent arrival Markovian service process

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Computing queue length and waiting time distributions in finite-buffer discrete-time multiserver queues with late and early arrivals

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2004年第10-11期48卷 1557-1573页

作者： Gupta, UC Samanta, SK Sharma, RK Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India Indian Inst Technol Dept Math New Delhi 110016 India

This paper presents modelling and analysis of discrete-time multiserver finite-buffer queue with general interarrival and geometric service time. Using the supplementary variable technique, and considering the remaining interarrival time as a supplementary variable, two variants of this model, namely the late arrival system with delayed access (LAS-DA) and early arrival system (EAS), have been examined. For both the cases, steady-state system length distributions at arbitrary, prearrival, and outside observer's observation epochs have been obtained. Further, the waiting time distribution in the queue is also discussed. Various performance measures such as probability of loss, average number of busy servers and average waiting time in the queue etc. have been presented. It is hoped that the results obtained in this paper may provide useful information to designers of telecommunication systems, practitioners, and others. (C) 2004 Elsevier Ltd. All rights reserved.

关键词： discrete-time finite-buffer multiserver queue

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Reducing congestion in bulk-service finite-buffer queueing system using batch-size-dependent service

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PERFORMANCE EVALUATION 2012年第1期69卷 53-70页

作者： Banerjee, A. Gupta, U. C. Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

In the design and analysis of any queueing system, one of the main objectives is to reduce congestion which can be achieved by controlling either arrival-rates or service-rates. This paper adopts the latter approach and analyzes a single-server finite-buffer queue where customers arrive according to the Poisson process and are served in batches of minimum size a with a maximum threshold limit b. The service times of the batches are arbitrarily distributed and depends on the size of the batches undergoing service. We obtain the joint distribution of the number of customers in the queue and the number with the server, and distributions of the number of customers in the queue, in the system, and the number with the server. Various performance measures such as the average number of customers in the queue (system) and with the server etc. are obtained. Several numerical results are presented in the form of tables and graphs and it is observed that batch-size-dependent service rule is more effective in reducing the congestion as compared to the one when service rates of the batches remain same irrespective of the size of the batch. This model has potential application in manufacturing, computer-communication network, telecommunication systems and group testing. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Batch-size-dependent service Bulk-service Congestion finite-buffer Queue

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Analysis of finite-buffer multi-server queues with group arrivals:: GI^X/M/c/N

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QUEUEING SYSTEMS 2000年第1-3期36卷 125-140页

作者： Laxmi, PV Gupta, UC Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

In this paper, we analyse a multi-server queue with bulk arrivals and finite-buffer space. The interarrival and service times are arbitrarily and exponentially distributed, respectively. The model is discussed with partial and total batch rejections and the distributions of the numbers of customers in the system at prearrival and arbitrary epochs are obtained. In addition, blocking probabilities and waiting time analyses of the first, an arbitrary and the last customer of a batch are discussed. Finally, some numerical results are presented.

关键词： bulk arrival finite-buffer multi-server queue waiting time

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A Low-Complexity Coded Transmission Scheme Over finite-buffer Relay Links

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IEEE TRANSACTIONS ON COMMUNICATIONS 2018年第7期66卷 2873-2887页

作者： Li, Ye Zhang, Shibing Wang, Jue Ji, Xiaodong Wu, Huangnan Bao, Zhihua Nantong Univ Sch Elect & Informat Nantong 226019 Peoples R China Nantong Res Inst Adv Commun Technol Nantong 226019 Peoples R China

Relay transmissions play an important role in many types of communication systems. In this paper, we consider packet-level coded transmissions over lossy relay links with the finite-buffer and coding coefficients delivery cost constraints. We propose a low-complexity coding scheme where packets are encoded from sequentially formed random subsets of source packets called batches. The relay recodes only from the buffered packets belonging to the same batch to maintain the code sparsity, lowering the packet header overhead and the decoding complexity compared to the random linear network coding (RLNC). To analyze the performance, we first propose an absorbing Markov chain model to analyze the RLNC transmission over finite-buffer relay links. The finite-length analysis not only provides a lower bound on the completion time using any sparser random codes but also characterizes each individual batch's transmission of the proposed code. Based on the analysis, another Markov chain is proposed to determine the decoding failure probability and the expected completion time of the batch coding scheme. As shown through analysis and simulations, the proposed scheme achieves higher effective end-to-end rates than RLNC when the coding coefficients delivery cost is considered and is also with much lowered decoding complexity thanks to its sparseness.

关键词： Relay finite-buffer sparse network codes decoding complexity absorbing Markov chain

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Analysis of finite-buffer discrete-time batch-service queue with batch-size-dependent service

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COMPUTERS & INDUSTRIAL ENGINEERING 2014年第1期75卷 121-128页

作者： Banerjee, A. Gupta, U. C. Goswami, V. Indian Inst Technol BHU Dept Math Sci Varanasi 221005 Uttar Pradesh India Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India KIIT Univ Sch Comp Applicat Bhubaneswar 751024 Orissa India

Over the last two decades there has been considerable growth in digital communication systems which operate on a slotted system. In several applications, transmission of packets over the network takes place in batches of varying size, and transmission time depends upon the size of the batch. Performance modelling of these systems is usually done using discrete-time queues. In view of this, we consider a single-server queue with finite-buffer in a discrete-time domain where the packets are transmitted in batches (of varying size) according to minimum and maximum threshold limit, usually known as general batch service rule. The transmission time (in number of slots) of these batches depends on the number of packets within the batch under transmission, and is arbitrarily distributed. We obtain, in steady-state, distribution of the number of packets waiting in the queue and in service (those being transmitted in batches). In addition, we also obtain average number of packets waiting in queue, in the system, with the server, rejection probabilities, etc. Finally, computational experiences with a variety of numerical results have been discussed by introducing a cost model which gives optimum value of the lower threshold limit. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Batch-size-dependent service Blocking probability Discrete-time finite-buffer Steady-state Queue

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Analyzing a multiserver bulk-service finite-buffer queue

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APPLIED MATHEMATICAL MODELLING 2008年第9期32卷 1797-1812页

作者： Goswami, V. Samanta, S. K. Laxmi, P. Vijaya Gupta, U. C. Kalinga Inst Ind Technol Dept Comp Sci Bhubaneswar 751024 Orissa India Jawaharlal Nehru Technol Univ Coll Engn Dept Math Kakinada 500072 India Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

This paper analyzes a finite-buffer multiserver bulk-service queueing system in which the interarrival and service times are, respectively, arbitrarily and exponentially distributed. Using the supplementary variable and the imbedded Markov chain techniques, we obtain the queue-length distributions at prearrival and arbitrary epochs. We also present LaplaceStiltjes transform of the actual waiting-time distribution in the queue. Finally, several performance measures and a variety of numerical results in the form of tables and graphs are discussed. (c) 2007 Elsevier Inc. All rights reserved.

关键词： bulk-service finite-buffer multiserver queue waiting-time

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On the finite-buffer bulk-service queue with general independent arrivals:: GI/M^[b]/1/N

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OPERATIONS RESEARCH LETTERS 1999年第5期25卷 241-245页

作者： Laxmi, PV Gupta, UC Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

We consider a single server finite-buffer bulk-service queue in which the interarrival and service times are arbitrarily and exponentially distributed, respectively. The service is performed in batches of maximum size b. The distributions of number of customers in the queue at pre-arrival and arbitrary epochs have been obtained. In addition, analysis of waiting time in the queue is also carried out. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： finite-buffer bulk-service blocking probability queue waiting time

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New results on bulk service queue with finite-buffer: M/G((a, b))/1/N

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OPSEARCH 2011年第3期48卷 279-296页

作者： Gupta, Umesh Banerjee, A. Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

We consider a single-server finite-buffer queue with general bulk service rule where customers arrive according to a Poisson process and service times of the batches are arbitrarily distributed. Using the embedded Markov chain technique we first obtain the steady-state joint distribution of the number of customers in the queue and number with the departing batch at departureepoch. Further in order to obtain the joint distribution of the number of customers in the queue and number with the server at arbitrary-epoch, we develop relations between arbitrary-and departure-epoch probabilities. Finally, we also obtain the distributions of number of customers in the queue (system), and number with the server. Various performance measures of interest such as average number of customers in the queue (system) and average number of customers with the server etc. are obtained. The model was earlier discussed by Gold and Tran-Gia (Queueing Syst 14: 413-426, 1993) and Chaudhry and Gupta (Queueing Syst 31: 95-100, 1999) wherein they first obtained the distribution of the number of customers in the queue at departure-epoch without taking into the consideration of the size of the departing batch. Then they obtained the distribution of the number of customers in the queue at arbitraryepoch when server is idle/busy.

关键词： Bulk-service finite-buffer Queue Blocking probability

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On the Consecutive Customer Loss Probabilities in a finite-buffer Renewal Batch Input Queue with Different Batch Acceptance/Rejection Strategies Under Non-renewal Service 7th

On the Consecutive Customer Loss Probabilities in a Finite-B...

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International Conference on Soft Computing for Problem Solving (SocProS)

作者： Banik, A. D. Ghosh, Souvik Chaudhry, M. L. Indian Inst Technol Bhubaneswar Sch Basic Sci Argul Campus Khurja 752050 Odisha India Royal Mil Coll Canada Dept Math & Comp Sci STN Forces POB 17000 Kingston ON K7K 7B4 Canada

ISBN: (纸本)9789811315923;9789811315916

This paper deals with a finite-buffer renewal input queueing system, where the arrivals occur in batches of random size and the server serves the customers singly. The successive service times are correlated and its representation is expressed through the continuous-time Markovian service process (C-MSP). As the buffer capacity is finite, the partial batch rejection policy and the total batch rejection policy are considered in this paper. The blocking probabilities and mean waiting time of the first, last, and an arbitrary customer of a batch are determined using the steady-state system-length distribution at pre-arrival epoch. Further, the probability of k or more consecutive customer loss (i.e., k-CCL) during a busy period is computed. The results are illustrated by some tables and graphs for different inter-batch-arrival distributions as well as different C-MSP representations.

关键词： Renewal batch-arrival finite-buffer Continuous-time Markovian service process (C-MSP) Blocking probabilities Consecutive customer losses (CCL)

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