Choosing among heterogeneous server clouds

A. Karthik (), Arpan Mukhopadhyay () and Ravi R. Mazumdar ()
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A. Karthik: University of Waterloo
Arpan Mukhopadhyay: University of Waterloo
Ravi R. Mazumdar: University of Waterloo

Queueing Systems: Theory and Applications, 2017, vol. 85, issue 1, No 1, 29 pages

Abstract: Abstract This paper considers a model of interest in cloud computing applications. We consider a multiserver system consisting of N heterogeneous servers. The servers are categorized into M( $$\ll N$$ ≪ N ) different types according to their service capabilities. Jobs having specific resource requirements arrive at the system according to a Poisson process with rate $$N \lambda $$ N λ . Upon each arrival, a small number of servers are sampled uniformly at random from each server type. The job is then routed to the sampled server with maximum vacancy per server capacity. If a job cannot obtain the required amount of resources from the server to which it is assigned, then the job is discarded. We analyze the system in the limit as $$N \rightarrow \infty $$ N → ∞ . This gives rise to a mean field, which we show has a unique fixed point and is globally attractive. Furthermore, as $$N\rightarrow \infty $$ N → ∞ , the servers behave independently. The stationary tail probabilities of server occupancies are obtained from the stationary solution of the mean field. Numerical results suggest that the proposed scheme significantly reduces the average blocking probability compared to static schemes that probabilistically route jobs to servers in proportion to the number of servers of each type. Moreover, the reduction in blocking holds even for systems at high load. For the limiting system in statistical equilibrium, our simulation results indicate that the occupancy distribution is insensitive to the holding time distribution and only depends on its mean.

Keywords: Heterogeneous servers; Multirate loss model; Mean field; Propagation of chaos; 60K35; 90B15; 60J27; 60J80 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11134-016-9488-8

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