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Operations Research, Systems Engineering and Industrial Engineering Commons

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Full-Text Articles in Operations Research, Systems Engineering and Industrial Engineering

Algorithmic Analysis Of The Maximum Level Length In General-Block Two-Dimensional Markov Processes, Jesus R. Artalejo, Srinivas R. Chakravarthy Jun 2005

Algorithmic Analysis Of The Maximum Level Length In General-Block Two-Dimensional Markov Processes, Jesus R. Artalejo, Srinivas R. Chakravarthy

Industrial & Manufacturing Engineering Publications

Two-dimensional continuous-time Markov chains (CTMCs) are useful tools for studying stochastic models such as queueing, inventory, and production systems. Of particular interest in this paper is the distribution of the maximal level visited in a busy period because this descriptor provides an excellent measure of the system congestion. We present an algorithmic analysis for the computation of its distribution which is valid for Markov chains with general-block structure. For a multiserver batch arrival queue with retrials and negative arrivals, we exploit the underlying internal block structure and present numerical examples that reveal some interesting facts of the system.


A Multi-Server Markovian Queueing Model With Primary And Secondary Services, Valentina Klimenok, Srinivas R. Chakravarthy, Alexander Dudin Jan 2005

A Multi-Server Markovian Queueing Model With Primary And Secondary Services, Valentina Klimenok, Srinivas R. Chakravarthy, Alexander Dudin

Industrial & Manufacturing Engineering Presentations And Conference Materials

We study a multi-server queueing model in which the arrivals occur according to a Markovian arrival process. An arriving customer either (a) is lost due to all main servers being busy; or (b) enters into service with one of the main servers and leaves the system (as a satisfied primary customer); (c) enters into a service with one of the main servers, gets service in self-service mode, and is impatient to get a final service with one of the main servers, may leave the system (as a dissatisfied secondary customer); or (d) enters into service with one of the main ...