Analysis of a Fork/Join Station with Inputs from a Finite Population: Sub-Network with Multi-Server Stations

KU Leuven Working Paper No. KBI 0619

25 Pages Posted: 12 Dec 2006

See all articles by Nico Goossens

Nico Goossens

OM Partners n.v.

Ananth Krishnamurthy

Rensselaer Polytechnic Institute (RPI) - Department of Decision Sciences and Engineering Systems

Nico Vandaele

Campus Kortrijk - Faculty of Applied Economics

Date Written: 2006

Abstract

This paper presents an exact analysis of a fork/join station with inputs from stations composed of multiple exponential servers. The queue length process at the input buffers is analyzed exactly in terms of the underlying Markov process. The semi-Markov kernel characterizing the departure process is analyzed to derive expressions for the marginal and joint distributions of inter-departure times from the fork/join station. These analyses are used to study the effect of inputs from multiple servers on key performance measures at a fork/join station. Comparison studies show that replacing the multiple servers by a single server with equivalent capacity could result insignificantly different estimates of throughput, synchronization delays and queue lengths at the individual buffers. These insights could lead to better representation of synchronization constraints in closed queuing network models of computer networks, fabrication/assembly systems and material control strategies for manufacturing systems.

Keywords: Assembly systems, Closed queuing networks, Fork/join, Synchronization, Processes, Buffers, Markov processes, Distribution, Time, Studies, Performance, Representation, Constraint, Queuing, Models, Model, Computer networks, Networks, Systems, Control, Strategy, Manufacturing

Suggested Citation

Goossens, Nico and Krishnamurthy, Ananth and Vandaele, Nico, Analysis of a Fork/Join Station with Inputs from a Finite Population: Sub-Network with Multi-Server Stations (2006). KU Leuven Working Paper No. KBI 0619. Available at SSRN: https://ssrn.com/abstract=950912 or http://dx.doi.org/10.2139/ssrn.950912

Nico Goossens

OM Partners n.v. ( email )

Koralenhoeve 23
Wommelgem / Antwerpen, 2160
Belgium

Ananth Krishnamurthy (Contact Author)

Rensselaer Polytechnic Institute (RPI) - Department of Decision Sciences and Engineering Systems ( email )

Troy, NY 12180
United States
1 518 2958 (Phone)
1 518 276 8227 (Fax)

Nico Vandaele

Campus Kortrijk - Faculty of Applied Economics ( email )

Etienne Sabbelaan 53
Kortrijk, B-8500
Belgium

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