In this paper, we present an analysis for an M/M/c/N queueing system with balking, reneging and synchronous vacations of partial servers together. It is assumed that arriving customers balk with a probability and renege according to an exponential distribution. The vacation policy prescribes that any d (0<d<c) servers take a vacation together when these d servers find that no customers are wait...

Abstract By applying the Takács’ technique about the busy period to the regenerative cycle method, this paper gives the strict proof for the time average distributions of the queue length in M/G/1 without depending on other methods. Moreover we extend its proof from the service time to the completion time(CT). That is, we choose the stochastic behavior on the completion time as the regenerative...

This paper investigates the steady state property of queue length for a batch arrival queue under N-policy with single vacation and setup times. When the system becomes empty, the server is turned off at once and takes a single vacation of random length V . When he returns, if the queue length reaches or exceeds threshold ( 1) N N  , the server is immediately turned on but is temporarily unava...

In this paper we present the analysis of the BMAP/GI/1 phase dependent vacation model with decrementing-K service discipline. The exhaustive discipline is a special case of the decrementing-K discipline, where K = ∞. The generalization of the service discipline independent expressions of the vacation model [7] for phase dependent vacation enables the treatment of the BMAP/GI/1 queue as special ...

Consider a single server fixed batch service queueing system under multiple vacation with a possibility of negative arrival in which the arrival rate λ follows a Poisson process, the service time follows an exponential distribution with parameter μ. Further we assume a negative arrival rate occur at the rate of ν which follows a Poisson process and the length of time the server in vacation foll...

In this paper, we present a discrete-time single-server finite-buffer queue in which the server takes single/multiple vacations whenever the system becomes empty. The interarrival times are geometrically distributed and service, vacation times are independently identically distributed random variables and their durations are integral multiples of a slot duration. We obtain the state probabiliti...