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Title Integral expressions for the numerical evaluation of product form expressions over irregular multidimensional integer state spaces
 
Names MANJUNATH, D
SIKDAR, B
Date Issued 1999 (iso8601)
Abstract Ill this paper 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 queueing networks, polymerization and genetic models where the system state is a vector of integers, n = [n(1),...,n(M)] and the steady state solution is Of the form pi(n) = Pi i = 1 (M) 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 and algorithmic solutions covering specific forms of f(i)((i)) and shapes of the space over which these are known. In this paper we derive general integral expressions for arbitrary state spaces and f(i)(n(i)). The expressions that we derive here become especially useful if the generating functions f(t)(n(t)) call be expressed as a ratio of polynomials in which case, exact closed form expressions can be obtained for the sums. The integral expressions that we derive here have wide applications and we demonstrate them by three examples in which we model finite highway cellular systems, copy networks in multicast packet switches and BCMP queueing networks.
Genre Proceedings Paper
Topic Normalizing Constants
Identifier PROCEEDINGS OF 1999 SYMPOSIUM ON PERFORMANCE EVALUATION OF COMPUTER AND TELECOMMUNICATION SYSTEMS,326-333