EXPONENTIAL BOUNDS FOR QUEUES WITH MARKOVIAN ARRIVALS

abstract

• Exponential bounds [queueb]{symbol}eb are found for queues whose increments are described by Markov Additive Processes. This is done by application of maximal inequalities to exponential martingales for such processes. Through a thermodynamic approach the constant is shown to be the decay rate for an asymptotic lower bound for the queue length distribution. The class of arrival processes considered includes a wide variety of Markovian multiplexer models, and a general treatment of these is given, along with that of Markov modulated arrivals. Particular attention is paid to the calculation of the prefactor {symbol}. 1994 J.C. Baltzer AG, Science Publishers.

authors

• Duffield, Nick

published proceedings

• QUEUEING SYSTEMS

author list (cited authors)

• DUFFIELD, N. G.

citation count

• 59

complete list of authors

• DUFFIELD, NG

publication date

• September 1994

publisher

• Springer Nature  Publisher

published in

• Queueing Systems  Journal

keywords

• Atm Multiplexers
• Effective Bandwidths
• Large Deviations
• Markov Additive Processes
• Martingales
• Queuing Theory
• Risk Theory

Digital Object Identifier (DOI)

• 10.1007/BF01158702

start page

• 413

end page

• 430

volume

• 17

issue

• 3-4

URL

• http://dx.doi.org/10.1007/bf01158702