Experimental results on matrix-analytical solution techniques–extensions and comparisons

We present a comprehensive numerical approach with reasonably light complexity in terms of implementation and computation for assessing the performance of hybrid make-to-stock (MTS)/make-to-order (MTO) systems. In such hybrid systems, semi-finished products are produced up front and stored in a decoupling inventory. When an order arrives, the products are completed and possibly customised. We study this system in a stochastic setting: demand and production are modelled by random processes. In particular, our model includes two coupled Markovian queues: one queue represents the decoupling inventory and the other the order backlog. These queues are coupled as order processing can only occur when both queues are non-empty. We rely on matrix analytic techniques to study the performance of the MTO/MTS system under non-restrictive stochastic assumptions. In particular, we allow for arrival correlation and non-exponential setup and MTS and MTO processing times, while the hybrid MTS/MTO system is managed by an (s,S)-type threshold policy that governs switching from MTO to MTS and back. By some numerical examples, we assess the impact of inventory control, irregular order arrivals, setup and order processing times on inventory levels and lead times.

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“…Several iterative procedures exist for solving Equation (4) above. For example, Gun [38] uses the following simple recursion:…”

Section: Quasi-birth-death Processmentioning

confidence: 99%

Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production

et al. 2020

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Performance study of ATM multicast switching systems

Chen

Lambadaris

Hayes

1995

Int J Communication

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We evaluate the performance of an N x N ATM discrete time multicast switch model with input queueing operating under two input access disciplines. First we present the analysis for the case of a purely random access discipline and subsequently we concentrate on a cyclic priority access based on a circulating token ring. In both cases, we focus on two HOL (head-of-line) packet service disciplines. Under the first (one-shot transmission discipline), all the copies generated by each HOL packet seek simultaneous transmission during the same time slot. Under the second service discipline (call-splitting), all HOL copies that can be transmitted in the same time slot are released while blocked copies compete for transmission in subsequent slots. In our analysis the performance measures introduced are the average packet delay in the input buffers as well as the maximum throughput of the switch. A significant part of the analysis is based on matrix geometric techniques. Finally, numerical results are presented and compared with computer simulations.

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Algorithms for Infinite Markov Chains with Repeating Columns

Latouche

1993

Linear Algebra, Markov Chains, and Queueing Models

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Abstract. We consider Markov chains on an infinite state space, with a lower blockHessenberg transition matrix. If the columns repeat as in the case of the G I / P H /1 queue, then the stationary probability vector is matrix-geometric. The major difficulty in computing the stationary vector resides in the determination of the solution of a non-linear matrix equation.Various algorithms may be used for that purpose. They are discussed, and their computational efficiency is compared. While most of the algorithms examined are well known, some are presented here for the first time.

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Experimental results on matrix-analytical solution techniques–extensions and comparisons

Cited by 34 publications

References 5 publications

Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production

Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production

Performance study of ATM multicast switching systems

Algorithms for Infinite Markov Chains with Repeating Columns

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