On the non-Markovian multiclass queue under risk-sensitive cost

Rami Atar and Gal Mendelson ()
Additional contact information
Rami Atar: Technion–Israel Institute of Technology
Gal Mendelson: Technion–Israel Institute of Technology

Queueing Systems: Theory and Applications, 2016, vol. 84, issue 3, No 3, 265-278

Abstract: Abstract This paper studies a control problem for the multiclass G/G/1 queue for a risk-sensitive cost of the form $$n^{-1}\log E\exp \sum _ic_iX^n_i(T)$$ n - 1 log E exp ∑ i c i X i n ( T ) , where $$c_i>0$$ c i > 0 and $$T>0$$ T > 0 are constants, $$X^n_i$$ X i n denotes the class-i queue length process, and the numbers of arrivals and service completions per unit time are of order n. The main result is the asymptotic optimality, as $$n\rightarrow \infty $$ n → ∞ , of a priority policy, provided that $$c_i$$ c i are sufficiently large. Such a result has been known only in the Markovian (M/M/1) case. The index which determines the priority is explicitly computed in the case of Gamma-distributed interarrival and service times.

Keywords: Multiclass G/G/1; Risk-sensitive control; Large deviations; 60F10; 60K25; 49N70; 93E20 (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11134-016-9503-0 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_s11134-016-9503-0

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

DOI: 10.1007/s11134-016-9503-0

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 ().