This paper considers discrete-time single-server queueing systems where the arrivals of cells are a timecorrelated arrival process and the service for cells is done every R slots. In particular, the arrivals is governed by a stationary Markov chain, where no arrivals are assumed to occur only when the Markov chain is in a particular state. A typical example of the arrival processes satisfying t...

For a sequence of nite Markov chains L(N) we introduce the notion of \conver-gence time to equilibrium" T(N). For sequences that are obtained by truncating some countable Markov chain L we nd the convergence time to equilibrium in terms of Lyapunov function of Markov chain L. We apply this result to queue-ing systems with a limited number of customers: a priority system with several customer ty...

This paper presents two methods to calculate the response time distribution of impatient customers in a discrete-time queue with Markovian arrivals and phase-type services, in which the customers’ patience is generally distributed (i.e., the D-MAP/PH/1 queue). The first approach uses a GI/M/1 type Markov chain and may be regarded as a generalization of the procedure presented in Van Houdt [14] ...

We consider a multiserver queuing process speciied by i.i.d. interarrival time, batch size and service time sequences. In the case that diierent servers have diierent service time distributions we say the system is heterogeneous. In this paper we establish conditions for the queuing process to be characterized as a geometrically Harris recurrent Markov chain, and we characterize the stationary ...

In this paper we study a single-server queue where the inter-arrival times and the service times depend on a common discrete time Markov Chain. This model generalizes the well-known MAP/G/1 queue by allowing dependencies between interarrival and service times. The waiting time process is directly analyzed by solving Lindley’s equation by transform methods. The Laplace Stieltjes transforms (LST)...

We consider a two-queue polling model in which customers upon arrival join the shorter of two queues. Customers arrive according to a Poisson process and the service times in both queues are independent and identically distributed random variables having the exponential distribution. The two-dimensional process of the numbers of customers at the queue where the server is and at the other queue ...

existence of capacity drop phenomenon, as the difference between pre-queue and queue discharge flow rates, has been one of the controversial concepts of traffic engineering. several researches have focused on capacity drop existence and also its estimation issues. this paper aims to estimate capacity drop based not only on a comparison between breakdown and queue discharge flow rates, but also ...

Abstract: This paper examines the steady state behavior of an M/G/1 queue with repeated attempts in which the server may provide an additional second phase of service. This model generalizes both the classical M/G/1 retrial queue and the M/G/1 queue with classical waiting line and second optional service. We carry out an extensive stationary analysis of the system, including existence of statio...

We consider a feedback finite fluid queue with downward jumps, where the net flow rate and the jump size for the fluid are controlled by a background Markov chain with a finite state space. The finite means that the fluid queue has a finite buffer. The feedback means that the transition structure of the background process may change when the buffer content becomes empty or full. In this paper, ...