By Jiang Libin, Walrand Jean

During this booklet, we examine the matter of accomplishing the utmost throughput and application in a category of networks with resource-sharing constraints. this can be a classical challenge of serious significance. within the context of instant networks, we first suggest a completely disbursed scheduling set of rules that achieves the utmost throughput. encouraged by means of CSMA (Carrier feel a number of Access), that is broadly deployed in ultra-modern instant networks, our set of rules is straightforward, asynchronous, and straightforward to enforce. moment, utilizing a singular maximal-entropy approach, we mix the CSMA scheduling set of rules with congestion keep an eye on to procedure the utmost application. additionally, we additional express that CSMA scheduling is a modular MAC-layer set of rules that may paintings with different protocols within the delivery layer and community layer. 3rd, for instant networks the place packet collisions are unavoidable, we determine a normal analytical version and expand the above algorithms to that case. Stochastic Processing Networks (SPNs) version production, conversation, and repair platforms. In production networks, for instance, projects require components and assets to provide different elements. SPNs are extra basic than queueing networks and pose novel demanding situations to throughput-optimum scheduling. We proposes a "deficit greatest weight" (DMW) set of rules to accomplish throughput optimality and maximize the web application of the creation in SPNs. desk of Contents: creation / assessment / Scheduling in instant Networks / software Maximization in instant Networks / dispensed CSMA Scheduling with Collisions / Stochastic Processing networks

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**Additional resources for Scheduling and Congestion Control for Wireless and Processing Networks (Synthesis Lectures on Communication Networks)**

**Example text**

F . The utility of that flow is uf (λf ). Each node i maintains a separate queue for each flow f of packets that go through it. The backlog in that queue is Xi,f . Let sj,f be the service rate of packets of flow f by link j . Let δf and f be the source and destination node of flow f . Consider the following problem: Maximize H (π) + β uf (λf ) f sj,f ≤ Subject to j :w(j )=i sj ,f , ∀f, i = δf , i = f , λf ≤ j :t (j )=i j :t (j )=δf sj,f ≤ sj (π ), and f sj ,f , ∀f, π(S) = 1. S In this problem, sj (π) is the average service rate of link j under the distribution π .

5 MAXIMAL-ENTROPY INTERPRETATION This section provides a different view of the above scheduling problem, which will help us later develop a number of other algorithms. It shows that the desired distribution of the independent sets has maximum entropy subject to serving the links fast enough. Accordingly, to generalize the algorithm of this chapter, one will add an entropy term to the objective function of more general problems. t. hj = K k=1 xk rk , ∀j rk ≥ 0, ∀k. 32 3. SCHEDULING IN WIRELESS NETWORKS j For each j = 1, 2, .

5), then the Lagrangian is L(r; d) = F (r; λ) + dT r. 3), is the service rate (at stationary distribution) given r. Since dk∗ ≥ 0, λk ≤ sk (r ∗ ). 7) where the KL divergence ¯ : = DKL (p||p(r)) = i [p¯ i log(p¯ i /pi (r))] [ p ¯ i i log(p¯ i )] − F (r; λ). That is, we choose r ≥ 0 such that p(r) is the “closest” to p¯ in terms of the KL divergence. , a moment-matching condition). In our case, the time-reversible CSMA Markov chain gives the product-form distribution. Also, the arrival rate and service rate on link k are viewed as two marginal probabilities.