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Optimization of M/M/s/N Queueing Model with reneging in a Fuzzy Environment

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American Journal of Operations Research 2021年第3期11卷 121-140页

作者： Ananda Prasad Panta Ram Prasad Ghimire Dinesh Panthi Shankar Raj Pant Department of Mathematics Tri-Chandra Campus Tribhuvan University Kathmandu Nepal Department of Mathematics Kathmandu University Kavre Nepal Department of Mathematics Valmeeki Campus Nepal Sanskrit University Kathmandu Nepal Central Department of Mathematics Tribhuvan University Kirtipur Nepal

This paper deals with the study of multi-server queueing model in a fuzzy environment with imposition of reneging of customers. Entry of the customers in the system is assumed to be Poisson process and exponential service time distribution under first-come-first-served basis. Specific of this investigation is to derive the various fuzzy performance measures such as fuzzy queue length, fuzzy waiting time in queue, fuzzy response time and fuzzy optimal number of servers in explicit form for the finite capacity multi-server queueing system by using recursive method. For the validity of the model we have obtained the numerical illustrations in tabular form which shows that fuzzy-queue can be more realistic than crisp queue.

关键词： Fuzzy Environment Poisson Optimal reneging

Effects of reneging, Server Breakdowns and Vacation on a Batch Arrival Single Server Queueing System with Three Fluctuating Modes of Service

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Open Journal of Optimization 2020年第4期9卷 105-128页

作者： Samuel Ugochukwu Enogwe H. Onyebuchi Obiora-Ilouno Department of Statistics Michael Okpara University of Agriculture Umudike Nigeria Department of Statistics Nnamdi Azikiwe University Awka Nigeria

This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability generating functions of the steady state probabilities of several states of the system including the steady state queue size distribution. Further, we discuss some particular cases of the proposed queueing model. We present numerical examples in order to demonstrate the effects of server vacation and reneging on the various states of the system. The study revealed that an increase in reneging and a decrease in server vacation results in a decrease in server utilization and an increase in server’s idle time provided rates of server breakdown and repair completion are constant. In addition, the probability of server vacation, the probability of system is under repair and the probabilities that the server provides service in three fluctuating modes decreases due to an increase in reneging and a decrease in vacation completion rates.

关键词： Queueing reneging Server Vacation Server Breakdowns Fluctuating Modes of Service

N-policy for M^(x)/G/1 Unreliable Retrial G-Queue with Preemptive Resume and Multi-services

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Journal of the Operations Research Society of China 2016年第4期4卷 437-459页

作者： Amita Bhagat Madhu Jain Department of Applied Sciences The Northcap UniversityGurgaon 122017India Department of Mathematics Indian Institute of Technology RoorkeeRoorkee 247667India

Bulk arrival retrial G-queue with impatient customers and multi-servicessubject to server breakdowns has been analyzed. The system allows the arrival oftwo types of customers: positive customers and negative customers in the *** negative customers make the server fail if they find the server in busy state,whereas positive customers are served if the server is idle otherwise they join thevirtual pool of customers called orbit. The customers from the retrial orbit try theirchance again for the service. The customers have the option of obtaining more than oneservice. Moreover, the customers are impatient and may renege from the system withprobability (1−r ). The server is sent for repair as soon as it breakdowns;after repair,the service process starts again. Also, the server has the provision to initiate the servicewhen there areN customers accumulated in the system. Using supplementary variablestechnique and generating functions, various performance measures like reliabilityindices and long run probabilities have been obtained.

关键词： Retrial queue N-policy vacation Negative customers reneging Bulk arrival Breakdowns Preemptive resume Multi-services

A Spectrum Occupancy Model for Primary Users in Cognitive Radio Systems

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Journal of Computer and Communications 2023年第11期11卷 78-86页

作者： Yingying Cao Yiqian Zhao Haihua Li School of Mathematics and Information Science Henan Polytechnic University Jiaozuo China

There are abundant research results related to cognitive radio systems (CR systems), but using queueing models to portray CR systems is a new research trend. In this paper, a single-server retrial cognitive radio system with a linear retrial rate has been considered. The system has two types of users: primary users and secondary users. Secondary users have no effect on primary users because primary users have preemptive precedence. As a result, our purpose is to examine some performance indicators such as the expected queue length for primary users, the probability of the system being idle or occupied by a secondary user, and the probability of the system being busy. This paper begins by deriving the expressions for the generating functions based on the balance equations, so that we can calculate our goal conveniently.

关键词： Cognitive Radio System Retrial Queue reneging Stable-State Distribution

Design and Analysis of Prioritized Medium Access Control Protocol for Backbone Routers in Wireless Mesh Networks

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Tsinghua Science and Technology 2012年第5期17卷 537-552页

作者： Lei Pan Hongyi Wu Qualcomm Inc. 1700 Technology Dr.San JoseCA 95110USA The Center for Advanced Computer Studies University of Louisiana at LafayetteLafayetteLA 70504USA

A Prioritized Medium Access Control （P-MAC） protocol is proposed for wireless routers of mesh networks with quality-of-service provisioning. The simple yet effective design of P-MAC offers strict service differentiation for prioritized packets. A Markov model is developed to yield important performance matrices including the packet blocking probability due to queue overflow and the packet reneging probability due to delay bound. It is further proved that the service time of P-MAC approximates exponential distribution, and can be effectively estimated. The analytic models with preemptive and non-preemptive schemes, validated via simulations, show that P-MAC can effectively support traffic differentiation and achieve very low packet dropping （both reneging and blocking） probabilities when the traffic load is below the channel capacity. When the network is overloaded, P-MAC can still maintain extremely stable and high channel throughput. Moreover, it is demonstrated that P-MAC performs superior in multihop networks, further proving the advantages of the proposed protocol.

关键词： Markov chain reneging medium access control binary countdown packet priorization network throughput Quality-of-Service (QoS) wireless mesh networks wireless routers