Pierre Le Gall, "Single server tandem queues and queueing networks with non-correlated successive service times", International Journal of Stochastic Analysis, vol. 14, Article ID 127089, 18 pages, 2001. https://doi.org/10.1155/S1048953301000338
Single server tandem queues and queueing networks with non-correlated successive service times
To evaluate the local actual queueing delay in general single server queueing networks with non-correlated successive service times for the same customer, we start from a recent work using the tandem queue effect, when two successive local arrivals are not separated by premature departures. In that case, two assumptions were made: busy periods not broken up, and there are limited variations for successive service times. These assumptions are given up after having crossed two stages. The local arrivals become indistinguishable for the sojourn time inside a given busy period. It is then proved that the local sojourn time of this tandem queue effect may be considered as the sum of two components: the first (independent of the local interarrival time) corresponding to the case where upstream, successive service times are supposed to be identical to the local service time, and the second (negligible after having crossed 2 or 3 stages) depending on local interarrival times increasing because of broken up busy periods. The consequence is the possible occurrence of the agglutination phenomenon of indistinguishable customers in the buffers (when there are limited premature departures), due to a stronger impact of long service times upon the local actual queueing delay, which is not consistent with the traditional concept of local traffic source only generating distinguishable customers.
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