In this paper, we consider a discrete-time finite-capacity queue with Bernoulli arrivals and batch services. In this queue, the single server has a variable service capacity and serves the customers only when the number of customers in system is at least a certain threshold value. For this queue, we first obtain the queue-length distribution just after a service completion, using the embedded M...

We consider a bulk service G I / M / l queue with service rates depending on service batch size. If there are n customers waiting at the completion of service, min(n, I\) customers enter service. We show that the queue size and the service batch size at points of arrivals form an embedded Markov chain and the steady-state probabilities of this Markov chain have the matrix geometric form. We des...

This paper studies a discrete-time single-server queue with two independent inputs and service interruptions. One of the inputs to the queue is an independent and identically distributed process. The other is a much more general process and it is not required to be Markov nor is it required to be stationary. The service interruption process is also general and it is not required to be Markov or...

Based on establishing the mathematical model of system provided parameters, using discrete-time Markov chain and a function set by non-negative integer random variable as Probabilistic methods, discrete time variable, two-queue different gated polling has been fully analyzed, low- higher-order properties cycle period are deduced, average queue pair length waiting delay for message packets calcu...

This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on-off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on pro...

We prove a functional central limit theorem for Markov additive arrival processes (MAAPs) where the modulating Markov process has the transition rate matrix scaled up by n (α > 0) and the mean and variance of the arrival process are scaled up by n. It is applied to an infinite-server queue and a fork-join network with a non-exchangeable synchronization constraint, where in both systems both the...

This paper analyzes a generic class of two-node queueing systems. A first queue is fed by an on–off Markov fluid source; the input of a second queue is a function of the state of the Markov fluid source as well, but now also of the first queue being empty or not. This model covers the classical two-node tandem queue and the two-class priority queue as special cases. Relying predominantly on pro...

Abstract. In this paper, the multi–server queue with general service time distribution and Lebesgue–dominated iid inter–arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the embedded Markov chain at arrival instants. The concept of piecewise–deterministic Markov processes is applied to model the inter–arrival behaviour. ...

We present an update formula that allows the expression of the deviation matrix of a continuous-time Markov process with denumerable state space having generator matrix Q∗ through a continuous-time Markov process with generator matrix Q. We show that under suitable stability conditions the algorithm converges at a geometric rate. By applying the concept to three different examples, namely, the ...

This paper studies a multi-server queueing system with multiple types of customers and last-come-®rst-served (LCFS) non-preemptive service discipline. First, a quasi-birth-and-death (QBD) Markov process with a tree structure is de®ned and some classical results of QBD Markov processes are generalized. Second, the MMAP[K]/PH[K]/N/LCFS non-preemptive queue is introduced. Using results of the QBD ...