Browsing by Author "Nain, P."
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Item Interchange Arguments in Stochastic Scheduling.(1988) Nain, P.; Walrand, J.; ISRInterchange arguments are applied to establish the optimality of priority list policies in three problems. First, we prove that in a multi-class tandem of two M 1 queues it is always optimal in the second node to serve according to the "c MU" rule. The result holds more generally if the first node is replaced by a multi- class network consisting of M 1 queues with Bernoulli routing. Next, for scheduling a single server in a multi-class node with feedback a simplified proof of Klimov's result is given. From it follows the optimality of the index rule among idling policies for general service time distributions, and among pre-emptive policies when the service time distributions are exponential. Lastly, we consider the problem of minimizing the blocking in a communication link with lossy channels and exponential holding times.Item On a Reduced Load Equivalence under Heavy Tail Assumptions(1998) Agrawal, Rakesh; Makowski, Armand M.; Nain, P.; ISR; CSHCNWe propose a general framework for obtaining asymptotic distributional bounds on the stationary backlog WA1+A2,c in a buffer fed by a combined fluid process A1+A2 and drained at a constant rate c.The fluid process A1 is an (independent) on-off source with average and peak rates r1 and r1, respectively, and with distribution G for the activity periods. The fluid process A2 of average rate r2 is arbitrary but independent of A1.
These bounds are used to identify subexponential distributions G and fairly general fluid processes A2 such that the asymptotic equivalence P[WA1+A2,c > x]~P[WA1,c-r2 > x](xלּ/font>/font>) holds under the stability condition r1+r2 < c and under the non-triviality condition c-r2 < r1.
The stationary backlog WA1,c-r2in these asymptotics results from feeding source A1 into a buffer drained at reduced rate c-r2. This reduced load asymptotic equivalence extends to a larger class of distributions G a result obtained by Jelenkovic and Lazar [18] in thecase when G belongs to the class of regular intermediatevarying distributions.
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