This paper considers the tail asymptotics for a cumulative process {B(t); t ≥ 0} sampled at a heavy-tailed random time T . The main contribution of this paper is to establish several sufficient conditions for the asymptotic equality P(B(T ) > bx) ∼ P(M(T ) > bx) ∼ P(T > x) as x → ∞, where M(t) = sup0≤u≤t B(u) and b is a certain positive constant. The main results of this paper can be used to ob...

In this paper we propose a novel MATLAB tool, called Q-MAM, to compute queue length, waiting time and sojourn time distributions of various discrete and continuous time queuing systems with an underlying structured Markov chain/process. The underlying paradigms include M/G/1and GI/M/1-type, quasi-birth-death and non-skip-free Markov chains (implemented by the SMCSolver tool), as well as Markov ...

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Abstract: This paper aims at presenting an alternate approach to derive the exact transient solution of Markovian queues. The continued fraction (Jacobi fraction) is expressed as power series and the power series coefficients are connected by a two-dimensional recurrence relation associated with infinite Stieltjes matrix equation. The recurrence relation is solved by using generating functions....

In the present paper, mathematical modeling for analyzing a Markovian queueing system with two heterogeneous servers and working vacation has been demonstrated. Keeping in view queueing situations in real life problems, here we consider service policy that initially both the heterogeneous servers take vacation when there are no customers waiting for service in the queue; however, after this ser...

In this paper we study a broad class of semi-Markovian queues introduced by Sengupta. This class contains many classical queues such as the GI/M/1 queue, SM/MAP/1 queue and others, as well as queues with correlated inter-arrival and service times. Queues belonging to this class are characterized by a set of matrices of size m and Sengupta showed that its waiting time distribution can be represe...

This paper studies a control problem for the multiclass G/G/1 queue for a risk-sensitive cost of the form n logE exp ∑ i ciX n i (T ), where ci > 0 and T > 0 are constants, X n i denotes the class-i queue length process, and the number of arrivals and service completions per unit time are of order n. The main result is the asymptotic optimality, as n → ∞, of a priority policy, provided that ci ...

The join-the-shortest-queue routing policy is studied in an asymptotic regime where the number of processors n scales with arrival rate. A large deviation principle (LDP) for occupancy process established, as n→∞, a suitable infinite-dimensional path space. Model features that present technical challenges include, Markovian dynamics discontinuous statistics, diminishing rate property transition...

We consider a uid queue receiving its input from the output of a Marko-vian queue with nite or innnite waiting room. The input rate of the uid queue is characterized by a Markov modulated rate process. We derive a new approach for the computation of the stationary buuer content. This approach leads to a numerically stable algorithm for which the precision of the result can be given in advance. ...