Analysis of Batch Arrival Single and Bulk Service Queue with Multiple Vacation Closedown and Repair

In this paper, we analyze batch arrival single and bulk service queueing model with multiple vacation, closedown and repair. The single server provides single service if the queue size is ‘\u3c a’ and bulk service if the queue size is ‘ ≥ a’. After completing the service (single or bulk), the server may breakdown with probability ξ and then it will be sent for repair. When the system becomes empty or the server is ready to serve after the repair but no one is waiting, the server resumes closedown and then goes for a multiple vacation of random length. Using supplementary variable technique, the steady-state probability generating function (PGF) of the queue size at an arbitrary time is obtained. The performance measures and cost model are also derived. Numerical illustrations are presented to visualize the effect of system parameters

Performance Analysis of an M/M/1 Queue with N-policy Interrupted Closedown Preventive Maintenance Balking and Feedback

This paper investigates the transient and stationary behavior of a M/M/1 queueing model with N-policy, interrupted closedown, balking, feedback and preventive maintenance. The server stays dormant (off state) until N customers accumulate in the queue and then starts an exhaustive service (on state). After the service, each customer may either leave the system or get immediate feedback. When the system becomes empty, the server resumes closedown. If any arrival occurs before the completion of closedown time, the closedown work of the server is interrupted and starts the busy period in an exhaustive manner. If no arrival occurs during the closedown time, the server commences preventive maintenance work. When this period ends, the server moves to the idle state and waits N accumulate for service. When the Nth one enters the queue, the server starts the service. The customers may either join the queue or balk when the size of the system is less than N and the server is in off state. The transient and stationary system size probabilities of the proposed model are derived by the method of generating function. Some system performance indices are computed and the numerical simulations are also presented

Transient analysis of a Markovian Single Vacation Feedback Queue with an Interrupted Closedown Time and Control of Admission During Vacation

This paper analyzes the transient behavior of an M/M/1 queueing model with single vacation, feedback, interrupted closedown time and control of admission during vacation. The time-dependent system size probabilities for the proposed model are obtained using generating function in the closed form. Further, the system performance measures like mean and variance of system size are also obtained for the time-dependent case. Finally, numerical illustrations are presented to understand the effect for various system parameters

Transient Solution of an M/M/1 Retrial Queue with Reneging from Orbit

In this paper, the transient behavior of an M/M/1 retrial queueing model is analyzed where the customers in the orbit possess the reneging behavior. There is no waiting room in the system for the arrivals. If the server is not free when the occurrence of an arrival, the arriving customer moves to the waiting group, known as orbit and retries for his service. If the server is idle when an arrival occurs (either coming from outside the queueing system or from the waiting group), the arrival immediately gets the service and leaves the system. Each individual customer in the orbit, retrying for his service, becomes impatient and starts reneging from the orbit. Here the reneging of customers is due to the long wait in the orbit. Using continued fractions, the transient probabilities of orbit size for this model are derived explicitly. Average and variance of orbit size at time t are also obtained. Further, numerical illustrations of performance measures are done to analyze the effect of parameters