Consider a Markov chain {X n } n≥0 with an ergodic probability measure π. Let Ψ be a function on the state space of the chain, with α-tails with respect to π, α ∈ (0, 2). We find sufficient conditions on the probability transition to prove convergence in law of N 1/α N n Ψ(X n) to an α-stable law. A " martingale approximation " approach and " coupling " approach give two different sets of condi...

We consider a markovian multiserver queue with a finite waiting line in which a customer may decide to leave and give up service if its waiting time in queue exceeds its random deadline. We focus on the performance measure in terms of the probability of being served under both transient and stationary regimes. We investigate monotonicity properties of first and second order of this performance ...

Abstract In this paper, recursive equations for waiting time distributions of r-th occurrence of a compound pattern are studied via the finite Markov chain imbedding technique under overlapping and non-overlapping counting schemes in sequences of independent and identically distributed (i.i.d.) or Markov dependent multi-state trials. Using the relationship between number of patterns and r-th wa...

We study a queueing system with a Poisson arrival process and Markov modulated, exponential service requirements. For a modulating Markov Chain with two states, we show that the distribution of the number-in-system is a superposition of two matrix-geometric series and provide a simple algorithm for computing the rate and coefficient matrices. These results hold for both finite and infinite wait...

Consider a Markov chain {X n } n≥0 with an ergodic probability measure π. Let Ψ a function on the state space of the chain, with α-tails with respect to π, α ∈ (0, 2). We find sufficient conditions on the probability transition to prove convergence in law of N 1/α N n Ψ(X n) to a α-stable law. A " martingale approximation " approach and " coupling " approach give two different sets of condition...

This paper presents a discrete-time single-server finite buffer N threshold policy queue with renewal input and discrete Markovian service process. The server terminates service whenever the system becomes empty, and recommences service as soon as the number of waiting customers in the queue is N . We obtain the system-length distributions at prearrival and arbitrary epochs using the supplement...

We derive a non-Markovian theory for waiting time distributions of consecutive single electron transfer events. The presented microscopic Pauli rate equation formalism couples the open electrodes to the many-body system, allowing to take finite bias and temperature into consideration. Numerical results reveal transient oscillations of distinct system frequencies due to memory in the waiting tim...

We consider a single-server first-in-first-out queue fed by a finite number of distinct sources of jobs. For a large class of short-range dependent and light-tailed distributed job processes, using functional large deviation techniques we prove a large deviation principle and logarithmic asymptotics for the joint waiting time and queue lengths distribution. We identify the paths that are most l...

We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals and regularly varying service time distribution with index −ν, it is shown that the waiting time distribution is also regularly varying, with index 1− ν, and...

Production parallel systems are space-shared and hence employ batch queues in which the jobs submitted to the systems are made to wait before execution. Thus, jobs submitted to parallel batch systems incur queue waiting times in addition to the execution times. Prediction of these queue waiting times is important to provide overall estimates to the users and can also help metaschedulers make sc...