We establish a unified analytical framework for load balancing systems, which allows us to construct a general class Π of policies that are both throughput optimal and heavy-traffic delay optimal. This general class Π includes as special cases popular policies such as join-shortest-queue and power-of-d, but not the join-idle-queue (JIQ) policy. In fact we show that JIQ, which is not in Π, is actually not heavy-traffic delay optimal. Owing to the significant flexibility offered by class Π, we are able to design a new policy called join-below-threshold (JBT-d), which maintains the simplicity of pull-based policies such as JIQ, but updates its threshold dynamically. We prove that JBT-d belongs to the class Π when the threshold is picked appropriately and thus it is heavy-traffic delay optimal. Extensive simulations show that the new policy not only has a low complexity in message rates, but also achieves excellent delay performance, comparable to the optimal join-shortest-queue in various system settings.The rest of the paper is organized as follows. Section 1.1 reviews the related work on load balancing schemes. Section 1.2 introduces the necessary notation in the paper. Section 2 describes the system model and the related definitions. Section 3 presents the main results of the paper. In particular, a class Π of flexible load balancing policies are introduced, containing as special cases the popular existing ones and motivating new ones. Sufficient conditions are derived to guarantee throughput and heavy-traffic delay optimality. Section 4 contains the simulation results on comparing different policies, demonstrating the performance and simplicity of our new policy. Section 5 contains the proof of the main results.
Related work: push versus pullThis section reviews state-of-the-art load balancing policies with a focus on the system performance in heavy traffic. We group these policies mainly into two categories: push-based and pull-based as shown in Fig. 1.Push-based policy: Under a push-based policy, the dispatcher tries to "push" jobs to servers. More specifically, upon each job arrival, the dispatcher sends probing messages to the servers, which feed back the required information for dispatching decisions, e.g., queue lengths. After receiving the feedback, the dispatcher sends the incoming jobs to servers based on a dispatching distribution. A classical example in this category is the JSQ policy, under which the dispatcher queries the queue length information of each server upon new job arrivals, and sends the incoming jobs to the server with the shortest queue, with ties broken randomly. It has been shown [19] that for homogeneous servers this policy is delay optimal in a stochastic ordering sense under the assumption of renewal arrival and non-decreasing failure rate service. In the heavy-traffic regime, it has been proved that it is heavy-traffic delay optimal for both heterogeneous and homogeneous servers [2]. Nevertheless, the performance of this policy comes at the cost of substantial overhead as it has to...
The network delay upper-bound analysis problem is of fundamental importance to real-time applications in Networkon-Chip (NoC). In the paper, we revisit a state-of-the-art analysis model for real-time communication in wormhole NoC with priority-based preemptive arbitration and show that the model may provide pessimistic or even incorrect network delay upper-bound. We then propose a revised analysis model to correct the flaws in the previous model by further classifying indirect interference as upstream and downstream indirect interferences according to the relative positions of traffic flows and taking buffer influence into consideration. Simulated evaluations show that our model provides tighter and correct network delay upper-bound compared with the state-of-the-art model.
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