An infinite server system with general packing constraints

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We consider a service system model primarily motivated by the problem of efficient assignment of virtual machines to physical host machines in a network cloud, so that the number of occupied hosts is minimized. There are multiple input flows of different type customers, with a customer mean service time depending on its type. There is an infinite number of servers. A server-packing configuration is the vector k = {ki}, where ki is the number of type i customers the server "contains." Packing constraints must be observed; namely, there is a fixed finite set of configurations k that are allowed. Service times of different customers are independent; after a service completion, each customer leaves its server and the system. Each new arriving customer is placed for service immediately; it can be placed into a server already serving other customers (as long as packing constraints are not violated), or into an idle server. We consider a simple parsimonious real-time algorithm, called Greedy, that attempts to minimize the increment of the objective function ΣkXk1+α, α > 0, caused by each new assignment; here Xk is the number of servers in configuration k. (When α is small, ΣkXk 1+α approximates the total number ΣkX k of occupied servers.) Our main results show that certain versions of the Greedy algorithm are asymptotically optimal, in the sense of minimizing Σk Xk1+α in stationary regime as the input flow rates grow to infinity. We also show that in the special case when the set of allowed configurations is determined by vector-packing constraints, the Greedy algorithm can work with aggregate configurations as opposed to exact configurations k, thus reducing computational complexity while preserving the asymptotic optimality.

Original languageEnglish (US)
Pages (from-to)1200-1217
Number of pages18
JournalOperations Research
Issue number5
StatePublished - Sep 2013
Externally publishedYes

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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