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SUMMARY:RESTART simulation of non-Markovian queuing networks - Villn-Altam
 irano\, M\, Villn-Altamirano\, J\, Vzquez Gallo\, E (Technical University 
 of Madrid)
DTSTART:20100622T101500Z
DTEND:20100622T104000Z
UID:TALK25318@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:The performance requirements of broadband communication networ
 ks are often expressed in terms of events with very low probability. Analy
 tical or numerical evaluation is only possible for a very restricted class
  of\nsystems. Crude simulations require prohibitively long execution times
  for the accurate estimation of very low probabilities\, and thus accelera
 tion methods are necessary.\n\nA more frequent occurrence of a formerly ra
 re event is achieved by performing a number of simulation retrials when th
 e process enters regions of the state space where the importance is greate
 r\, i.e.\, regions where the\nchance of occurrence of the rare event is hi
 gher. These regions\, called importance regions\, are defined by comparing
  the value taken by a function of the system state\, the importance functi
 on\, with certain thresholds.\nFormulas for the importance function of gen
 eral Jackson networks in [1].\n\nIn [2] networks with Erlang service times
  with different shape parameters were studied. The rare set was defined as
  the number of customers in a target node exceeding a predefined threshold
 . Two models were studied: a network with 7 nodes all of them at 	extquote
 dblleft distance	extquotedblright 1 or 2 from the target node and a 3-queu
 e tandem network with the loads of the first and second queue much greater
  than the\nload of the third queue. Low probabilities were accurately esti
 mated within short computational times in both models.\n\nIn this paper we
  extend the simulation study made in [2] in a twofold direction. On the on
 e hand we also simulate two additional types of networks that also could h
 ave difficulties for rare event simulation: a large network with 15 nodes\
 , some of them at 	extquotedblleft distance	extquotedblrightgreater than 2
 \, and a network with 2 nodes and very strong feedback. On the other hand 
 we use different non-exponential distributions as hyperexponential and Erl
 ang for modelling the interarrival and/or service times. This study will g
 ive us more insight for finding importance functions that could lead to go
 od estimates of the probability of interest in most networks.\n\n%ibliogr
 aphy{}\n\n[1] Vill'{e}n-Altamirano J. 2010. Importance functions for RESTA
 RT\nsimulation of general Jackson networks. European Journal of Operation\
 nResearch\, 203 (1): 156-165.\n\n[2]Vill'{e}n-Altamirano J. 2009. RESTART 
 Simulation of Networks of Queues\nwith Erlang Service Times. Proc. Winter 
 Simulation Conference\, Austin (USA)\,\n1146-1154.\n
LOCATION:Seminar Room 1\, Newton Institute
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