Control of Fork-Join Processing Networks with Multiple Job Types and Parallel Shared Resources

A fork-join processing network is a queueing network in which tasks associated with a job can be processed simultaneously. Fork-join processing networks are prevalent in computer systems, healthcare, manufacturing, project management, justice systems, and so on. Unlike the conventional queueing networks, fork-join processing networks have synchronization constraints that arise because of the parallel processing of tasks and can cause significant job delays. We study scheduling in fork-join processing networks with multiple job types and parallel shared resources. Jobs arriving in the system fork into arbitrary number of tasks, then those tasks are processed in parallel, and then they join and leave the network. There are shared resources processing multiple job types. We study the scheduling problem for those shared resources (i.e., which type of job to prioritize at any given time) and propose an asymptotically optimal scheduling policy in diffusion scale.

On the Optimal Control of Parallel Processing Networks with Resource Collaboration and Multitasking

We study scheduling control of parallel processing networks in which some resources need to simultaneously collaborate to perform some activities and some resources multitask. Resource collaboration and multitasking give rise to synchronization constraints in resource scheduling when the resources are not divisible, that is, when the resources cannot be split. The synchronization constraints affect the system performance significantly. For example, because of those constraints, the system capacity can be strictly less than the capacity of the bottleneck resource. Furthermore, the resource scheduling decisions are not trivial under those constraints. For example, not all static prioritization policies retain the maximum system capacity, and the ones that retain the maximum system capacity do not necessarily minimize the delay (or, in general, the holding cost). We study optimal scheduling control of a class of parallel networks and propose a dynamic prioritization policy that retains the maximum system capacity and is asymptotically optimal in diffusion scale and a conventional heavy-traffic regime with respect to the expected discounted total holding cost objective.

Exploring the Dynamical Behavior of Information Diffusion in D2D Communication Environment

This paper is dedicated to exploring the dynamical behavior of information diffusion in the Device-to-Device (D2D) communication environment for information security, so as to study how to accelerate the dissemination of beneficial information and curb the spread of malicious information. A mathematical model of information diffusion considering the combined impact of user awareness and social tie between users is proposed. The equilibrium of the model and its stability are fully analyzed. Very importantly, there is a unique (viral) equilibrium that is globally asymptotically stable without any preconditions. This means that the spread of malicious information in the D2D communication environment cannot be completely eliminated whatever measures are taken, but its diffusion scale can be controlled by adjusting the value of the equilibrium, and then the goal of pursuing the best control effect at the minimum cost can be achieved. In the same way, the dissemination scale of beneficial information can be expanded. Finally, the obtained main theoretical results are illustrated by some examples, and some suggestions are also given.

Subdiffusive Load Balancing in Time-Varying Queueing Systems

The degree to which delays or queue lengths equalize under load-balancing algorithms gives a good indication of their performance. Some of the most well-known results in this context are concerned with the asymptotic behavior of the delay or queue length at the diffusion scale under a critical load condition, where arrival and service rates do not vary with time. For example, under the join-the-shortest-queue policy, the queue length deviation process, defined as the difference between the greatest and smallest queue length as it varies over time, is at a smaller scale (subdiffusive) than that of queue lengths (diffusive).

An extended clustering method using H-index and minimum distance for searching multiple key spreaders

Identifying multiple key spreaders in a network can effectively control the diffusion of information and optimize the use of available resources, which can be also called the influence maximization problem in sociology domains. In order to maximize collective influence in complex networks, multiple spreaders must have both large single influence and small overlapping influence, but it is rather difficult to satisfy these two conditions simultaneously. In this paper, we try to achieve the best compromise between importance and dispersibility for multiple spreaders through clustering. The cluster centers are surrounded by nodes with lower influence, and the distance among different cluster centers is relatively far. In addition, the initial centers selection directly affects the efficiency of clustering and the realization of global optimization. Consequently, we present an initial centers selection algorithm combining H-index and minimum distance. The experimental results on four actual datasets show that the proposed method has better performance than the traditional benchmark methods in terms of transmission speed, diffusion scale and structural characteristics.

Universality of load balancing schemes on the diffusion scale

We consider a system of N parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any, and to a server with the shortest queue among d randomly selected servers otherwise (1≤d≤N). This load balancing scheme subsumes the so-called join-the-idle queue policy (d=1) and the celebrated join-the-shortest queue policy (d=N) as two crucial special cases. We develop a stochastic coupling construction to obtain the diffusion limit of the queue process in the Halfin‒Whitt heavy-traffic regime, and establish that it does not depend on the value of d, implying that assigning tasks to idle servers is sufficient for diffusion level optimality.