Max-Plus Linear Stochastic Systems and Perturbation Analysis by Bernd F. Heidergott

By Bernd F. Heidergott

This ebook presents a radical evaluation and clarification of the speculation of stochastic max-plus linear platforms, which has noticeable swift advances within the final decade. The insurance comprises modeling concerns and balance conception for stochastic max-plus platforms, perturbation research of max-plus platforms, constructing a calculus for differentiation of max-plus structures. This results in numerical reviews of functionality indices of max-plus linear stochastic structures, corresponding to the Lyapunov exponent or ready times.

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Extra info for Max-Plus Linear Stochastic Systems and Perturbation Analysis (The International Series on Discrete Event Dynamic Systems)

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A node consists of two kinds of places: service and buffer places. ' When an item arrives at a node and receives no service place, it has to wait for service on a buffer place. In the following we give a precise description of the dynamics of a generic queueing network. We consider a queueing network with J nodes. If items arrive at the network from the outside and leave the network, we call the network open, otherwise we call it closed. To facilitate considering both the open and the closed case, we assume that there is only one stream of arrivals.

Both versions of the system are max-plus linear with fixed support, that is, there exists A^{k) and A^(k), so that x^(k + 1) = A^{k) ® x^{k) represents the time evolution under n^ and x'^{k + 1) = A^lk) ® x^{k) that under n^. Now assume that after the fc*'' departure epoch the system runs under normal load with probability p and under reduced load with probability 1 — p. Define A{k) so that P{A{k) = A^k)) = p and P{A{k) = A^{k)) = 1 - p, then x{k -t- 1) = A{k) ® x{k) models the window flow control scheme with stochastic change of load.

Define A{k) so that P{A{k) = A^k)) = p and P{A{k) = A^{k)) = 1 - p, then x{k -t- 1) = A{k) ® x{k) models the window flow control scheme with stochastic change of load. In particular, A{k) fails to have fixed support, which stems from the fact that the support of A^{k) and A'^{k) doesn't coincide. 6 B o u n d s and Metrics 49 Another example of this kind is the multi-server queue with a variable number of servers modeling breakdowns of servers. 5. Observe that the multi-server queue with breakdowns fails to have fixed support.

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