EXPONENTIAL UPPER-BOUNDS VIA MARTINGALES FOR MULTIPLEXERS WITH MARKOVIAN ARRIVALS Academic Article

abstract

• We obtain explicit upper bounds in closed form for the queue length in a slotted time FCFS queue in which the service requirement is a sum of independent Markov processes on the state space {0, 1}, with integral service rate. The bound is of the form [queue length for any where c < 1 and y > 1 are given explicitly in terms of the parameters of the model. The model can be viewed as an approximation for the burst-level component of the queue in an ATM multiplexer. We obtain heavy traffic bounds for the mean queue length and show that for typical parameters this far exceeds the mean queue length for independent arrivals at the same load. We compare our results on the mean queue length with an analytic expression for the case of unit service rate, and compare our results on the full distribution with computer simulations.

authors

• Duffield, Nick

published proceedings

• JOURNAL OF APPLIED PROBABILITY

author list (cited authors)

• BUFFET, E., & DUFFIELD, N. G.

citation count

• 26

complete list of authors

• BUFFET, E||DUFFIELD, NG

publication date

• December 1994

publisher

• Cambridge University Press (CUP)  Publisher

published in

• Journal of Applied Probability  Journal

keywords

• Atm Multiplexers
• Heavy Traffic Limit
• Queuing Theory

Digital Object Identifier (DOI)

• 10.2307/3215328

start page

• 1049

end page

• 1060

volume

• 31

issue

• 4

URL

• http://dx.doi.org/10.2307/3215328