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Papers by Wondewosen Kassahun

Research paper thumbnail of Analysis of variant working vacation queue with reneging under a multi-server environment

international journal of management science and engineering management, Aug 28, 2019

This paper analyses an M/M/c queueing system with variant working vacations. The service times du... more This paper analyses an M/M/c queueing system with variant working vacations. The service times during regular busy periods, working vacation periods and vacation times are exponentially distributed and are mutually independent. During working vacation, customers may renege due to impatience and the impatient timer follows an exponential distribution. We derive the probability generating function of the steady-state probabilities and obtain some performance measures. The cost function associated with the model is also constructed and its optimization is investigated using quadratic fit search method. We have also presented the numerical illustrations of the effect of some parameters on the performance measures using graphs.

Research paper thumbnail of Performance measures of variant working vacations on batch arrival queue with server breakdowns

international journal of management science and engineering management, Jul 19, 2018

This paper analyzes an M X =M=1 variant working vacation queue with server breakdowns and repair.... more This paper analyzes an M X =M=1 variant working vacation queue with server breakdowns and repair. The server takes working vacations as soon as the system becomes empty. The service times during regular busy period, working vacation period, vacation times, breakdown times and repair times are all assumed to be exponentially distributed and are mutually independent. We have used the probability generating functions to derive the steady-state probabilities and obtain the closed form expressions of the system size. In addition, we obtain some other performance measures and their monotonicity with respect to variant working vacations.

Research paper thumbnail of • a Multi-Server Infinite Capacity Markovian Feedback Queue with Balking, Reneging and Retention of Reneged Customers

W e consider a multi-server infinite capacity Markovian feedback queue with reneging, balking and... more W e consider a multi-server infinite capacity Markovian feedback queue with reneging, balking and retention of reneged customers in which the inter-arrival and service times follow exponential distribution. The reneging times are assumed to be exponentially distributed. After the completion of service, each customer may rejoin the system as a feedback customer for receiving another regular service with a certain probability. A reneged customer can be retained in many cases by employing certain convincing mechanisms to stay in queue for completion of service. Numerical analysis, cost-profit analysis and optimization of the cost function using simulated annealing method are carried out. The steady-state solution of the model is obtained iteratively. Some performance measures are also derived.

Research paper thumbnail of Analysis of a Markovian queueing system with single working vacation and impatience of customers

Journal of Physics: Conference Series, 2019

In this paper, we study an infinite capacity single server Markovian queue with a single working ... more In this paper, we study an infinite capacity single server Markovian queue with a single working vacation and reneging of impatient customers in the queue during working vacation period. Customers arrive to the system following a Poisson distribution. The server goes to vacation when the system is empty and stay in vacation for a random period of time that is exponentially distributed. During the working vacation period, the server still continue providing service with a slow service rate. After the completion of the vacation, the server returns back to the regular service period and continue providing service with the regular busy period service rate if there are one or more customers in the system or it will stay idle until a new customer arrives to the system. During working vacation, customers in the queue get impatient and renege from the system and the reneging time is assumed to follow an exponential distribution. The system is modeled as a quasi-birth-death process and the s...

Research paper thumbnail of Analysis of variant working vacation queue with reneging under a multi-server environment

International Journal of Management Science and Engineering Management, 2019

This paper analyses an M/M/c queueing system with variant working vacations. The service times du... more This paper analyses an M/M/c queueing system with variant working vacations. The service times during regular busy periods, working vacation periods and vacation times are exponentially distributed and are mutually independent. During working vacation, customers may renege due to impatience and the impatient timer follows an exponential distribution. We derive the probability generating function of the steady-state probabilities and obtain some performance measures. The cost function associated with the model is also constructed and its optimization is investigated using quadratic fit search method. We have also presented the numerical illustrations of the effect of some parameters on the performance measures using graphs.

Research paper thumbnail of Transient analysis of multi-server Markovian queueing system with synchronous multiple working vacations and impatience of customers

International Journal of Mathematics in Operational Research, 2019

In this paper, we study an infinite capacity multi-server Markovian queue with synchronous multip... more In this paper, we study an infinite capacity multi-server Markovian queue with synchronous multiple working vacations, balking and reneging. It is assumed that customers may balk and/or renege with some probability if all the c servers are busy serving customers either during the regular busy period or working vacation period. The reneging times follow an exponential distribution. The system is modeled by a quasi-birth-death process and the transient-state probabilities of the model are obtained in the Laplace domain using matrix geometric method.

Research paper thumbnail of Analysis of variant working vacation queue with reneging under a multi-server environment

international journal of management science and engineering management, Aug 28, 2019

This paper analyses an M/M/c queueing system with variant working vacations. The service times du... more This paper analyses an M/M/c queueing system with variant working vacations. The service times during regular busy periods, working vacation periods and vacation times are exponentially distributed and are mutually independent. During working vacation, customers may renege due to impatience and the impatient timer follows an exponential distribution. We derive the probability generating function of the steady-state probabilities and obtain some performance measures. The cost function associated with the model is also constructed and its optimization is investigated using quadratic fit search method. We have also presented the numerical illustrations of the effect of some parameters on the performance measures using graphs.

Research paper thumbnail of Performance measures of variant working vacations on batch arrival queue with server breakdowns

international journal of management science and engineering management, Jul 19, 2018

This paper analyzes an M X =M=1 variant working vacation queue with server breakdowns and repair.... more This paper analyzes an M X =M=1 variant working vacation queue with server breakdowns and repair. The server takes working vacations as soon as the system becomes empty. The service times during regular busy period, working vacation period, vacation times, breakdown times and repair times are all assumed to be exponentially distributed and are mutually independent. We have used the probability generating functions to derive the steady-state probabilities and obtain the closed form expressions of the system size. In addition, we obtain some other performance measures and their monotonicity with respect to variant working vacations.

Research paper thumbnail of • a Multi-Server Infinite Capacity Markovian Feedback Queue with Balking, Reneging and Retention of Reneged Customers

W e consider a multi-server infinite capacity Markovian feedback queue with reneging, balking and... more W e consider a multi-server infinite capacity Markovian feedback queue with reneging, balking and retention of reneged customers in which the inter-arrival and service times follow exponential distribution. The reneging times are assumed to be exponentially distributed. After the completion of service, each customer may rejoin the system as a feedback customer for receiving another regular service with a certain probability. A reneged customer can be retained in many cases by employing certain convincing mechanisms to stay in queue for completion of service. Numerical analysis, cost-profit analysis and optimization of the cost function using simulated annealing method are carried out. The steady-state solution of the model is obtained iteratively. Some performance measures are also derived.

Research paper thumbnail of Analysis of a Markovian queueing system with single working vacation and impatience of customers

Journal of Physics: Conference Series, 2019

In this paper, we study an infinite capacity single server Markovian queue with a single working ... more In this paper, we study an infinite capacity single server Markovian queue with a single working vacation and reneging of impatient customers in the queue during working vacation period. Customers arrive to the system following a Poisson distribution. The server goes to vacation when the system is empty and stay in vacation for a random period of time that is exponentially distributed. During the working vacation period, the server still continue providing service with a slow service rate. After the completion of the vacation, the server returns back to the regular service period and continue providing service with the regular busy period service rate if there are one or more customers in the system or it will stay idle until a new customer arrives to the system. During working vacation, customers in the queue get impatient and renege from the system and the reneging time is assumed to follow an exponential distribution. The system is modeled as a quasi-birth-death process and the s...

Research paper thumbnail of Analysis of variant working vacation queue with reneging under a multi-server environment

International Journal of Management Science and Engineering Management, 2019

This paper analyses an M/M/c queueing system with variant working vacations. The service times du... more This paper analyses an M/M/c queueing system with variant working vacations. The service times during regular busy periods, working vacation periods and vacation times are exponentially distributed and are mutually independent. During working vacation, customers may renege due to impatience and the impatient timer follows an exponential distribution. We derive the probability generating function of the steady-state probabilities and obtain some performance measures. The cost function associated with the model is also constructed and its optimization is investigated using quadratic fit search method. We have also presented the numerical illustrations of the effect of some parameters on the performance measures using graphs.

Research paper thumbnail of Transient analysis of multi-server Markovian queueing system with synchronous multiple working vacations and impatience of customers

International Journal of Mathematics in Operational Research, 2019

In this paper, we study an infinite capacity multi-server Markovian queue with synchronous multip... more In this paper, we study an infinite capacity multi-server Markovian queue with synchronous multiple working vacations, balking and reneging. It is assumed that customers may balk and/or renege with some probability if all the c servers are busy serving customers either during the regular busy period or working vacation period. The reneging times follow an exponential distribution. The system is modeled by a quasi-birth-death process and the transient-state probabilities of the model are obtained in the Laplace domain using matrix geometric method.