Estimation of buffer overflow probabilities and economies of scale in ATM multiplexers by analysis of a model of packetized voice traffic

Farrell, Paul J.
(1999)
Estimation of buffer overflow probabilities and economies of scale in ATM multiplexers by analysis of a model of packetized voice traffic.
PhD thesis, Dublin City University.

We obtain upper bounds on the probability of buffer overflow for an ATM multiplexer of L identical packetized voice sources. The multiplexer is modelled by a FCFS single server queue. The arrivals at the multiplexer are a homogenous superposition of the arrivals from L independent identical sources, with each source modelled by a copy of a discrete time Markov Chain which we call the Cell Level Model. Throughout, appropriate parameters are scaled with L, to maintain a constant load over all superposition sizes.
The probability that, the queue-length (q^) of the queue in a finite buffer exceeds the buffer size b, is bounded above by the probability that the queue-length (qL) of the queue m an infinite buffer exceeds length b In order to bound the former above, we find upper bounds or approximations for the latter by using the theory of,
• Large Deviations, to determine its asymptotics for large b,
• Martingales, to obtain upper bounds, valid for all positive b,
• Large Deviations, to determine its asymptotics for large L for time rescaled
(proportional to L) arrival processes.
These demonstrate the multiplexing gam and economies of scale obtainable from large and small buffers and large multiplexers, respectively.

Item Type:

Thesis (PhD)

Date of Award:

1999

Refereed:

No

Supervisor(s):

Buffet, Emmanuelle

Uncontrolled Keywords:

ATM; Asynchronous transfer mode; Broadband networks