Linear loss networks

  • Authors:
  • Petar Momčilović;Mark S. Squillante

  • Affiliations:
  • Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA 32611;Mathematical Sciences Department, IBM T.J. Watson Research Center, Yorktown Heights, USA 10598

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2011

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Abstract

This paper investigates theoretical properties of throughput and cost in linear loss networks. The maximum throughput of the network with exponential service times is derived and the arrival process that maximizes throughput, given a fixed arrival rate, is established. For general service times, an asymptotically critical loading regime is identified such that the probability of an arbitrary customer being lost is strictly within (0,1) as the network size increases. This regime delivers throughput comparable to the maximum at a relatively low network cost. The paper establishes the asymptotic throughput and network cost under this critical loading.