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- Title
On the non-Markovian multiclass queue under risk-sensitive cost.
- Authors
Atar, Rami; Mendelson, Gal
- Abstract
This paper studies a control problem for the multiclass G/G/1 queue for a risk-sensitive cost of the form $$n^{-1}\log E\exp \sum _ic_iX^n_i(T)$$ , where $$c_i>0$$ and $$T>0$$ are constants, $$X^n_i$$ 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 $$n\rightarrow \infty $$ , of a priority policy, provided that $$c_i$$ 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.
- Subjects
QUEUEING networks; QUEUING theory; LARGE deviations (Mathematics); PRODUCTION scheduling; GAMMA distributions
- Publication
Queueing Systems, 2016, Vol 84, Issue 3/4, p265
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-016-9503-0