Exact Aggregation in Exponential Queueing Networks

Hendrik T. Vantilborgh

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Advanced Queuing Theory Analysis Probability and Statistical Research Petri Nets in System Modeling

Abstract

Aggregation as often used for the mvestlgat~on of large systems This techmqu¢ is pamculafly attracuve for nearly completely decomposable systems It as essentmlly an approxunate method, but at remains attractave since the error ,s small and bounds for at can be obtamed We are concerned here w,th aggregauon m exponential queuemg network analysas, and more precisely wath the condmons under which aggregation will yaeld exact results KEY WORDS AND PHRASES aggregation, eqmhbnum probabdlty vector, exponenual state-dependent server, Perron-Frobemus e~genvector, queuemg network CR CATEGORIES, 5 5, 5 19

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References

1975Open, Closed, and Mixed Networks of Queues with Different Classes of Customers 1963Jobshop-Like Queueing Systems 1975Parametric Analysis of Queuing Networks

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1993A generalization of Norton's theorem for queueing networks 1980Approximate Solution of Queueing Models 1987A Network Decomposition Approach for Approximating the Steady-State Behavior of Markovian Multi-Echelon Reparable Item Inventory Systems 1997Near Complete Decomposability: Bounding the Error by a Stochastic Comparison Method 2007Centralized Wireless Data Networks With User Arrivals and Departures 1998Norton's equivalent for queueing networks comprised of quasireversible components linked by state-dependent routing 1983Computational aspects of aggregation in multiple class queueing networks 1985Product-Form Synthesis of Queueing Networks

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