This paper analyzes large deviation probabilities related to the number of customers in a Markov modulated infinite-server queue, with state-dependent arrival and service rates. Two specific scalings are studied: in the first, just the arrival rates are linearly scaled by N (for large N ), whereas in the second in addition the Markovian background process is sped up by a factor N , for some > 0...

A new queue, referred to here as the HetSigma queue, in the Markovian framework, is proposed in order to model nodes in modern telecommunication networks. The queue has many of the necessary ingredients, such as joint (or individual) Markov modulation of the arrival and service processes, superposition of K CPP (compound Poisson process) streams of (positive) customer arrivals, and a CPP of neg...

This paper deals with analytical concepts for performance evaluation of packet switching mobile radio networks. A realistic characterisation of source traffic with means of marked Markovian arrival processes (MMAP) serves as an input process for a queuing model. The analysis of this model permits to derive the quantities of interest and allows to determine the achievable quality of service, whi...

A multi-class c-server retrial queueing system in which customers arrive according to a class-dependent Markovian arrival process (MAP) is considered. Service and retrial times follow class-dependent phase-type (PH) distributions with the further assumption that PH distributions of retrial times are acyclic. A necessary and sufficient condition for ergodicity is obtained from criteria based on ...

Formal languages with semantics based on ordinary differential equations (ODEs) have emerged as a useful tool to reason about large-scale distributed systems. We present differential bisimulation, a behavioral equivalence developed as the ODE counterpart of bisimulations for languages with probabilistic or stochastic semantics. We study it in the context of a Markovian process algebra. Similarl...

A stochastic model for a mobile network is studied. Users enterthe network, and then perform independent Markovian routes between nodes,where they receive service according to the Processor-Sharing policy. Oncetheir service requirement is satisfied, they leave the system. The stability re-gion is identified via a fluid limit approach, and strongly relies on a “spatialhomogen...

The application of Queuing Theory to quantify the relationships between trajectory uncertainties due to aviation operations, precision of navigation and control, and traffic flow efficiency in the National Airspace System is discussed. This work builds on a previous research effort on Markovian queuing network models of the NAS. While the Markovian network model provides closed-form analytical ...

This paper studies a single-stage production system, two-stage production system where specification limits are designed for inspection. When quality characteristics fall below a lower threshold or above an upper threshold, a decision is made to rework or scrap the item. The target is to determine the optimum target for a process based on rework or scrap costs. In contrast to previous studies, ...

This paper introduces an analytical method for approximating the performability of a firm realtime system modeled by a multi-server queue. The service discipline in the queue is earliestdeadline-first (EDF), which is an optimal scheduling algorithm. Real-time jobs with exponentially distributed relative deadlines arrive according to a Poisson process. All jobs have deadlines until the end of se...

One of the most important quantities of the exact Markovian SIS epidemic process is the time-dependent prevalence, which is the average fraction of infected nodes. Unfortunately, the Markovian SIS epidemic model features an exponentially increasing computational complexity with growing network size N . In this paper, we evaluate a recently proposed analytic approximate prevalence function intro...