Steady-state analysis of shortest expected delay routing

Jori Selen (), Ivo Adan (), Stella Kapodistria () and Johan Leeuwaarden ()
Additional contact information
Jori Selen: Eindhoven University of Technology
Ivo Adan: Eindhoven University of Technology
Stella Kapodistria: Eindhoven University of Technology
Johan Leeuwaarden: Eindhoven University of Technology

Queueing Systems: Theory and Applications, 2016, vol. 84, issue 3, No 6, 309-354

Abstract: Abstract We consider a queueing system consisting of two nonidentical exponential servers, where each server has its own dedicated queue and serves the customers in that queue FCFS. Customers arrive according to a Poisson process and join the queue promising the shortest expected delay, which is a natural and near-optimal policy for systems with nonidentical servers. This system can be modeled as an inhomogeneous random walk in the quadrant. By stretching the boundaries of the compensation approach we prove that the equilibrium distribution of this random walk can be expressed as a series of product forms that can be determined recursively. The resulting series expression is directly amenable to numerical calculations and it also provides insight into the asymptotic behavior of the equilibrium probabilities as one of the state coordinates tends to infinity.

Keywords: Heterogeneous servers; State-dependent routing; Multidimensional Markov process; Equilibrium distribution; Compensation approach; 60K25; 68M20; 60J27 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://link.springer.com/10.1007/s11134-016-9497-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:queues:v:84:y:2016:i:3:d:10.1007_s11134-016-9497-7

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/11134/

DOI: 10.1007/s11134-016-9497-7

Access Statistics for this article

Queueing Systems: Theory and Applications is currently edited by Sergey Foss

More articles in Queueing Systems: Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().