Multiproduct Queueing Networks with Deterministic Routing: Decomposition Approach and the Notion of Interference

Abstract

Queueing networks have been used to model the performance of a variety of complex systems. Since exact results exist for only a limited class of networks, the decomposition methodology has been used extensively to obtain approximate results. In this paper, we consider open queueing networks with multiple product classes, deterministic routings and general arrival and service distributions. We examine the decomposition method for such systems and show that it provides estimates of key parameters with an accuracy that is not acceptable in many practical settings. Recognizing this weakness, we enrich the approach by modeling a phenomenon previously ignored. We consider interference among products and describe its effect on the variance of the departure streams. The recognition of this effect significantly improves the performance of this methodology. We provide extensive experimental results based on the data of a manufacturer of semiconductor devices.queues: networks, queues: approximations, networks/graphs: multicommodity

Stochastic analysis of versatile workcentres

“…The authors propose three approximations for this purpose, which may be briefly stated as follows: (i) the arrivals of the aggregate product may be treated as Poisson; (ii) during any interarrival period of the part type i (aggregate part type), the interarrival process of the aggregate part type (part type i) may be treated as Erlangian; and (iii) the arrival of part type i is treated as a random incidence in the arrival stream of the aggregate product; both the part type i and the aggregate part type have Erlang arrivals. Extensive numerical investigations by Bitran & Tirupati (1988) indicate that the proposed approximations provide significant improvements in accuracy over the aggregation approach previously employed. In a subsequent paper (Bitran & Tirupati 1989), they develop an approximate analysis for a single workcentre multiple-item system, where the arriving workpieces of the different part types have to form a batch of a given (fixed) size before service can be started.…”

“…This is also useful in approximate analysis of non-productform open general queueing networks of automated manufacturing systems, by adapting the product-form networks idea of decomposing the network into independent nodes corresponding to machining centres. Approximate analysis of general open queueing networks, and further refinements, have been proposed based on this independence concept by several authors - Kuehn (1979), Marie (1979), Whitt (1983), Shanthikumar & Buzacott (1981 and Bitran & Tirupati (1988, 1989. In particular, the investigations of Shanthikumar and Buzacott, and Bitran and Tirupati are directed towards general open queueing network models of manufacturing systems, the former dealing with single product networks, and the latter with multi-product networks.…”

“…In the approach of the earlier papers, the system performance measures are obtained for a 'typical' part type, which is representative of all the part types; in a recently developed alternative approach (particularly Bitran & Tirupati 1988, 1990, performance measures are obtained for each part type individually by simplifying the system into a two-part type system: one part type is the particular part type of interest, and the second is an aggregate part type representative of all the other part types. the arrivals wait in an infinite capacity queue common to all part types, from which workpieces are taken up for machining on a first-come-first-served basis.…”

Differential evolution to solve the lot size problem in stochastic supply chain management systems

“…The queueing approach is similar to Lambrecht et al (1998), who on their turn have included some additional features into queueing approximations found in the literature (Shanthikumar and Buzacott 1981;Buzacott and Shanthikumar 1985;Shanthikumar and Sumita 1988;Bitran and Tirupati 1988). One of their main contribution is the approximation of the lead time distribution by a lognormal distribution, which is used to estimate a safety lead time such that customer orders are satisfied with a predefined service probability.…”

Due Date Management Policies

“…Most papers use hypothetical job-shop environments in simulations or use analytical models with very limiting assumptions. Exceptions include [67], which tests the proposed methods in a real-world example taken from [13]; [108], which discusses order acceptance and DDM practices at Lithonia Lighting, a lighting Þxture manufacturer; and [100], which reports results from a survey of 24 make-to-order Þrms (subcontracting component manufacturers and manufacturers of capital equipment) in the U.K on these Þrms' pricing and lead time quotation practices.…”