We devise an approximation of the marginal queue length distribution in discrete-time polling systems with batch arrivals and fixed packet sizes. The polling server uses the Bernoulli service discipline and Markovian routing. The 1-limited and exhaustive service disciplines are special cases of the Bernoulli service discipline, and traditional cyclic routing is a special case of Markovian routi...

We consider a discrete-time single-server queue with arrivals governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. This assumption implies that o -periods in the arrival process are i.i.d. and geometrically distributed. For this queue, we establish the exact relationship between queue length distributions in a nite-bu...

In this paper, we discuss the waiting-time distribution for a finite-space, single-server queueing system, in which customers arrive singly following Poisson process and server operates under (a,b)-bulk service rule. The system has finite-buffer capacity ‘N’ excluding batch service. service-time of batches follows general distribution, is independent arrival process. We first develop an alterna...

An embedded Markov chain is used to analyze a G/M/1 queuing system with N policy. When the system is empty, the server remains idle (deactivates) and does not start serving the waiting customers in the queue until the number of arrivals reaches N. The service is performed in batches of min(n, N) if there are n customers waiting at the completion of service. Service times of the server depend o...

In this paper we describe G/G/R+s multi- repairmen machining system with balking. The system consists of M operating machines, S spare machines, R permanent and s additional repairmen. Assuming the discrete flow of machines by continuous one, the diffusion approximation technique for the machine repair system has developed. The system will be in normal working mode if there is M operating machi...

In this paper, an M/G/1 queue model with the multiple adaptive vacations and pure decrementing service policy is studied based on the classical M/G/1 queueing model. The PGF of stationary queue length is derived by using an embedded Markov chain method. The LST of stationary waiting time is also given according to the independence between waiting time and arrival process. The average probabilit...

In this paper, we consider a BMAP/G/1 retrial queue with a server subject to breakdowns and repairs, where the life time of the server is exponential and the repair time is general. We use the supplementary variable method, which combines with the matrix-analytic method and the censoring technique, to study the system. We apply the RG-factorization of a level-dependent continuous-time Markov ch...

In this paper, we analyze a leaky bucket (LB) scheme with queue length dependent arrival rates. In other words, if the queue length exceeds an appropriate threshold value on buffer, the arrivals need to be controlled. In ATM networks, if the congestion occurs, the input traffics must be controlled (reduced) for congestion resolution. By the bursty and correlated properties of traffics, the arri...

In many industrial situations, machines are subjected to random breakdowns. In this paper, we consider the asynchronous vacation policy for the multi-server machine repair problem with server breakdown and two types of spares. According to this policy, when a certain number of servers become idle at a service completion instant, the servers will take an asynchronous vacation of random length to...

This paper presents the analysis of a finite buffer renewal input queue wherein the customers can decide either to join the queue with a probability or to balk. The service process is Markovian service process (MSP ) governed by an underlyingm-state Markov chain. Employing the supplementary variable and embedded Markov chain techniques, the steadystate system length distributions at pre-arrival...