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Integral expressions for the numerical evaluation of product form expressions over irregular multidimensional integer state spaces

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Title Integral expressions for the numerical evaluation of product form expressions over irregular multidimensional integer state spaces
 
Creator MANJUNATH, D
SIKDAR, B
 
Subject queuing-networks
normalizing constants
product form solutions
queuing networks
normalizing constant
 
Description We consider stochastic systems defined over irregular, multidimensional, integer spaces that have a product form steady state distribution. Examples of such systems include closed and BCMP type of queuing networks, polymerization and genetic models. In these models the system state is a vector of integers, n = [n(1),..,, n(M)] and the steady state solution has product form of the type pi (n) = Pi (M)(i=l) f(i) (n(i)). To obtain useful statistics from such product form solutions, pi (n) has to be summed over some subset of the space over which it is defined. We consider situations when these subsets are defined by a set of equalities and inequalities with integer coefficients, as is most often the case and provide integral expressions to obtain these sums. Typically, a brute force technique to obtain the sum is computationally very expensive. Algorithmic solutions are available for only specific forms of f(i)(n(i)) and shapes of the state space. In this paper we derive general integral expressions for arbitrary state spaces and arbitrary f(i) (n(i)). The expressions that we derive here become especially useful if the generating functions f(i) (n(i)) can be expressed as a ratio of polynomials in which case, exact closed form expressions can be obtained for the sums. We demonstrate the wide applicability of the integral expressions that we derive here through three examples in which we model finite highway cellular systems, copy networks in multicast packet switches and a BCMP queuing network modeling a multiuser computer system.
 
Publisher BALTZER SCI PUBL BV
 
Date 2011-10-22T01:32:20Z
2011-12-15T09:10:39Z
2011-10-22T01:32:20Z
2011-12-15T09:10:39Z
2001
 
Type Article; Proceedings Paper
 
Identifier TELECOMMUNICATION SYSTEMS,16,195-215
1018-4864
http://dx.doi.org/10.1023/A:1009067215525
http://dspace.library.iitb.ac.in/xmlui/handle/10054/14784
http://hdl.handle.net/100/1573
 
Source Symposium on Performance Evaluations of Computer and Telecommunications Systems (SPECTS 99),CHICAGO, ILLINOIS,JUL 11-15, 1999
 
Language English