Approximate analysis of load dependent general queueing networks

Abstract

Abstracf-A method for approximate solutions to load dependent closed queueing networks containing general service time distributions and FCFS scheduling disciplines is presented. The technique demonstrated is an extension of the well-known method of Marie. A new formula for the conditional throughputs is derived. After each iteration a check is performed to guarantee that the results obtained are within a tolerance level E . These iterations are repeated whenever invalid results are detected. On the average, the solutions obtained vary by less than 5 percent from their respective exact and simulation results.

Facilitating load-dependent queueing analysis through factorization

“…We first evaluate e ρ(N ) (v) by approximating the solution of a multiclass fixed-rate model to estimate the ρ(N ) vector, which may be done by using standard AMVA methods for fixed-rate models to determine the throughputs X σ (N ), e.g., AQL [19]. After computing ρ(N ), we are ready to determine the V single-class LLD normalizing constants e ρ(N ) (v) using a normalizing constant evaluation method for single-class LD or LLD models, such as (8) or (9).…”

“…Load-dependent service rates are also of theoretical interest for analyzing moments of performance Email addresses: g.casale@imperial.ac.uk (Giuliano Casale), p.harrison@imperial.ac.uk (Peter G. Harrison), wai.ong11@imperial.ac.uk (Ong Wai Hong) metrics [7], to evaluate networks with state-dependent routing [8], non-product form systems [9], fork-join networks [10], and to apply the flow-equivalent server method [11].…”

Queueing analysis for operations modeling in port logistics

“…This could be accomplished by resorting to a decomposition procedure based on (Marie, 1979;Yao and Buzacott, 1986;Akyildiz and Sieber, 1988) for an accurate approximate analysis. The procedure, later referred to as state-dependent exponential decomposition (SDED), is based on the following two assumptions for each station of the closed network:…”

Activity routing in a distributed supply chain: Performance evaluation with two inputs

“…A method for obtaining approximate solutions to load-dependent closed queuing networks containing general service-time distributions and first-come-first-served scheduling disciplines is presented in Akyildiz and Sieber (1998), and a formula for the throughput is derived. Ghosal et al (1989) present analytical results of computation-communication issues in dynamic dataflow architectures.…”

“…The generality of the RTP technique is illustrated by developing solution procedures for several important queuing systems which violate product form assumptions (Akyildiz and Sieber, 1998).…”