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 mo...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.展开更多
The author concerned the reliability evaluation as well as queueing analysis of M1, M2/G1, G2/1 retrial queues with two different types of primary customers arriving according to independent Poisson flows. In the case...The author concerned the reliability evaluation as well as queueing analysis of M1, M2/G1, G2/1 retrial queues with two different types of primary customers arriving according to independent Poisson flows. In the case of blocking, the first type of customers can be queued whereas the second type of customers must leave the service area but return after some random period of time to try their luck again. The author assumes that the server is unreliable and it has a service-type dependent, exponentially distributed life time as well as a service-type dependent, generally distributed repair time. The necessary and sufficient condition for the system to be stable is investigated. Using a supplementary variable method, the author obtains a steady-state solution for queueing measures, and the transient as well as the steady-state solutions for reliability measures of interest.展开更多
An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a P...An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served （FCFS） discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained.展开更多
Developing a comprehensive service strategy to optimize customer satisfaction presents an ongoing challenge for effective facility provider.The essence of comprehensive systems is selecting the suitable service design...Developing a comprehensive service strategy to optimize customer satisfaction presents an ongoing challenge for effective facility provider.The essence of comprehensive systems is selecting the suitable service design,establishing an effective service delivery process,and building continuous improvement.This research analyzes a finite capacity service system incorporating several realistic customer-server dynamics:customer impatience,server’s partial breakdown,and threshold recovery policy.When the number of customers is more,the server is under pressure to increase the service rate to mitigate the service system’s load.Motivating from this fact,the concept of service pressure condition is also incorporated.For characterization,we evaluate state probabilities derived using the matrix-analytic method and henceforth several performance measures.To address the cost optimization problem involving the developed Chapman-Kolmogorov forward differential-difference equations and determine optimal operational parameters,we employ the recently devised cuckoo search(CS)optimization approach.A comparative analysis is performed with the semi-classical optimizer:quasi-Newton(QN)method,and metaheuristics technique:particle swarm optimization(PSO),to validate the efficacy of results.Lastly,several numerical illustrations are depicted in different tables and graphs to understand essential characteristics quickly.展开更多
文摘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.
基金the Scientific Research Foundation for the Returned Overseas Chinese ScholarsEducation Ministry and the National Natural Science Foundation of China under Grant Nos 10526004 and 60504016
文摘The author concerned the reliability evaluation as well as queueing analysis of M1, M2/G1, G2/1 retrial queues with two different types of primary customers arriving according to independent Poisson flows. In the case of blocking, the first type of customers can be queued whereas the second type of customers must leave the service area but return after some random period of time to try their luck again. The author assumes that the server is unreliable and it has a service-type dependent, exponentially distributed life time as well as a service-type dependent, generally distributed repair time. The necessary and sufficient condition for the system to be stable is investigated. Using a supplementary variable method, the author obtains a steady-state solution for queueing measures, and the transient as well as the steady-state solutions for reliability measures of interest.
基金Research sponsored by BJTU Research Foundation (2005SM064),the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Education Ministry and the National Natural Science Foundation of China (10526004,60504016).
文摘An M/G/1 retrial queue with two-phase service and feedback is studied in this paper, where the server is subject to starting failures and breakdowns during service. Primary customers get in the system according to a Poisson process, and they will receive service immediately if the server is available upon arrival. Otherwise, they will enter a retrial orbit and are queued in the orbit in accordance with a first-come-first-served （FCFS） discipline. Customers are allowed to balk and renege at particular times. All customers demand the first “essential” service, whereas only some of them demand the second “multi-optional” service. It is assumed that the retrial time, service time and repair time of the server are all arbitrarily distributed. The necessary and sufficient condition for the system stability is derived. Using a supplementary variable method, the steady-state solutions for some queueing and reliability measures of the system are obtained.
基金The third author(MD)extends his sincere thanks to the funding agency CSIR-UGC,India,for the financial support(SRF/NET 1081/(CSIR-UGC NET DEC.2018)).
文摘Developing a comprehensive service strategy to optimize customer satisfaction presents an ongoing challenge for effective facility provider.The essence of comprehensive systems is selecting the suitable service design,establishing an effective service delivery process,and building continuous improvement.This research analyzes a finite capacity service system incorporating several realistic customer-server dynamics:customer impatience,server’s partial breakdown,and threshold recovery policy.When the number of customers is more,the server is under pressure to increase the service rate to mitigate the service system’s load.Motivating from this fact,the concept of service pressure condition is also incorporated.For characterization,we evaluate state probabilities derived using the matrix-analytic method and henceforth several performance measures.To address the cost optimization problem involving the developed Chapman-Kolmogorov forward differential-difference equations and determine optimal operational parameters,we employ the recently devised cuckoo search(CS)optimization approach.A comparative analysis is performed with the semi-classical optimizer:quasi-Newton(QN)method,and metaheuristics technique:particle swarm optimization(PSO),to validate the efficacy of results.Lastly,several numerical illustrations are depicted in different tables and graphs to understand essential characteristics quickly.
