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Technical Reports Authored or Co-authored by Prof. Armand M. Makowski
Papers resulting from CSHCN-related research are periodically added to the Institute for Systems Research Technical Report Database where they can be browsed by year or searched by author or keywords.
TCP Traffic Modeling via Limit Theorems (CSHCN TR 2002-13) by Peerapol Tinnakornsrisuphap, Armand M. Makowski
Traditional TCP traffic modeling has focused on "micro-scale" modeling of TCP, i.e., detailed modeling of a single TCP flow. While micro-scale models of TCP are suitable for understanding the precise behavior of individual flows, they are not well suited to the situation when a large number of TCP flows interact with each other as is the case in realistic networks.
In this survey, we present several works which focus on "macro-scale" modeling of TCP, where the aggregate behavior of TCP traffic can be simplified by applications of limit theorems.
Queue Dynamics of RED Gateways under Large Number of TCP Flows (CSHCN TR 2001-7) by Peerapol Tinnakornsrisuphap, Armand M. Makowski
We consider a stochastic model of a RED gateway under competing TCP-like sources sharing the capacity. As the number of competing flows becomes large, the queue behavior of RED can be described by a two-dimensional recursion. We confirm the result by simulations and discuss their implications for the network dimensioning problem.
Bounding On-Off Sources -- Variability Ordering and Majorization to the Rescue (CSHCN TR 2001-6) by Armand M. Makowski
We consider the problem of bounding the loss rates of the aggregation of on-off sources in a bufferless model by the loss rates associated with the aggregation of i.i.d. on-off sources. We use well-known results from the theory of variability orderings to establish a conjecture of Rasmussen et. al., a recent upper bound of Mao and Habibi, and to discuss a new conjectured upper bound by these authors.
On a Random Sum Formula for the Busy Period of the M|G|Infinity Queue with Applications (CSHCN TR 2001-4) by Armand M. Makowski
A random sum formula is derived for the forward recurrence time associated with the busy period length of the M|G|infinity queue. This result is then used to (1) provide a necessary and sufficient condition for the subexponentiality of this forward recurrence time, and (2) establish a stochastic comparison in the convex increasing (variability) ordering between the busy periods in two M|G|infinity queues with service times comparable in the convex increasing ordering.
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