Timeout control in distributed systems using Perturbation Analysis

Timeout control in distributed systems using perturbation analysis: Multiple communication links

“…We showed how a SFM of a timeout-controlled distributed system can be obtained and then used to optimize the timeout threshold. This paper extends the results in [17] to multiple communication links and hence, extends this problem to broader multi-class problems with communication delays. Like [17], we directly control the timeout parameters for network communication performance.…”

“…Moreover, according to (17),α n (t − θ n , θ ) = r n if w n (t − θ n , θ ) < θ n (i.e., node n not in a TOP n at t − θ n ). Noting that ∂ (t−θ n ) ∂ θ j = −1 only if j = n and 0, otherwise, we find…”

“…We do not include other states in the IPA calculations as by (25) and Lemma 1, they can be calculated in terms of the derivatives of x and α: A) Analysis at event times: We start by finding the derivative update equation of α n (t, θ ). Notice that unlike [17] where α n (t, θ ) was a continuous function of time, here, by definition α n (t, θ ) has a discontinuity whenever event [w n > θ n ] occurs. In general, we have the following lemma: Lemma 3.…”

“…where by (17), we get f α n (τ − k , θ ) − f α n (τ + k , θ ) = 0 − r n = −r n . Using this information in (27) proves the lemma.…”

“…In [17], we set forth a line of research aimed at quantifying how timeout threshold parameters affect the system state and ultimately its behavior and performance. We adopted a communication system model consisting of one transmitter submitting packets to a network with stochastic processing times.…”