Departure Processes from GI/GI/infinity and GI/GI/c/c with Bursty Arrivals

作者：Machihara Fumiaki^*; Tokuda Taro

来源：IEICE TRANSACTIONS ON COMMUNICATIONS, 2017, E100B(7): 1115-1123.

DOI：10.1587/transcom.2016EBP3297

• GI/GI/infinity
• GI/GI/c/c
• bursty arrival
• relation between arrival and departure
• entropy
• paradoxical behavior

When the random variable has a completely monotone density function, we call it bursty (BRST) random variable. At first, we prove that the entropy of inter-arrival time is smaller than or equal to the entropy of inter-departure time in an infinite-server system GI/G/infinity having general renewal arrivals. On the basis of that result, we prove that a BRST/GI/infinity having bursty arrivals and the associated loss system BRST 'Glick have the following paradoxical behavior: In the BRS T /GI/infinity, the stationary number of customers as well as the inter-departure time become stochastically less variable, as the service time becomes stochastically more variable. Also for the loss system BRST/GI/c/c, the blocking probability decreases and the inter-departure time becomes stochastically less variable, as the service time becomes stochastically more variable.

• 出版日期2017-7