2,961 research outputs found

    Load Balancing in the Non-Degenerate Slowdown Regime

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    We analyse Join-the-Shortest-Queue in a contemporary scaling regime known as the Non-Degenerate Slowdown regime. Join-the-Shortest-Queue (JSQ) is a classical load balancing policy for queueing systems with multiple parallel servers. Parallel server queueing systems are regularly analysed and dimensioned by diffusion approximations achieved in the Halfin-Whitt scaling regime. However, when jobs must be dispatched to a server upon arrival, we advocate the Non-Degenerate Slowdown regime (NDS) to compare different load-balancing rules. In this paper we identify novel diffusion approximation and timescale separation that provides insights into the performance of JSQ. We calculate the price of irrevocably dispatching jobs to servers and prove this to within 15% (in the NDS regime) of the rules that may manoeuvre jobs between servers. We also compare ours results for the JSQ policy with the NDS approximations of many modern load balancing policies such as Idle-Queue-First and Power-of-dd-choices policies which act as low information proxies for the JSQ policy. Our analysis leads us to construct new rules that have identical performance to JSQ but require less communication overhead than power-of-2-choices.Comment: Revised journal submission versio

    Scheduling over Scenarios on Two Machines

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    We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that scenario and all scenarios are given explicitly. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. With this research into optimization problems over scenarios, we have opened a new and rich field of interesting problems.Comment: To appear in COCOON 2014. The final publication is available at link.springer.co

    Enhancing the power of two choices load balancing algorithm using round robin policy

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    This paper proposes a new version of the power of two choices, SQ(d), load balancing algorithm. This new algorithm improves the performance of the classical model based on the power of two choices randomized load balancing. This model considers jobs that arrive at a dispatcher as a Poisson stream of rate lambdan,lambda<1, at a set of n servers. Using the power of two choices, the dispatcher chooses some d constant for each job independently and uniformly from the n servers in a random way and sends the job to the server with the fewest number of jobs. This algorithm offers an advantage over the load balancing based on shortest queue discipline, because it provides good performance and reduces the overhead in the servers and the communication network. In this paper, we propose a new version, shortest queue of d with randomization and round robin policies, SQ-RR(d). This new algorithm combines randomization techniques and static local balancing based on a round-robin policy. In this new version, the dispatcher chooses the d servers as follows: one is selected using a round-robin policy, and the d&#8722;1 servers are chosen independently and uniformly from the n servers in a random way. Then, the dispatcher sends the job to the server with the fewest number of jobs. We demonstrate with a theoretical approximation of this approach that this new version improves the performance obtained with the classical solution in all situations, including systems at 99% capacity. Furthermore, we provide simulations that demonstrate the theoretical approximation developed.This work was partially supported by the Project ‘‘CABAHLA-CM: Convergencia Big data-Hpc: de los sensores a las Aplicaciones’’ S2018/TCS-4423 from Madrid Regional Government

    Makespan Minimization via Posted Prices

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    We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: the ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm. We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms

    Randomized longest-queue-first scheduling for large-scale buffered systems

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    We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling algorithm by establishing new mean-field limit theorems as the number of buffers n→∞n\to\infty. We achieve this by allowing the number of sampled buffers d=d(n)d=d(n) to depend on the number of buffers nn, which yields an asymptotic `decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of nn and d(n)d(n). To our knowledge, we are the first to derive diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized longest-queue-first algorithm emulates the longest-queue-first algorithm, yet is computationally more attractive. The analysis of the system performance as a function of d(n)d(n) is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized longest-queue-first scheduling algorithm

    Load Balancing via Random Local Search in Closed and Open systems

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    In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach to an arbitrary server, but may switch server independently at random instants of time in an attempt to improve their service rate. This approach to load balancing contrasts with traditional approaches where clients make smart server selections upon arrival (e.g., Join-the-Shortest-Queue policy and variants thereof). Load resampling is particularly relevant in scenarios where clients cannot predict the load of a server before being actually attached to it. An important example is in wireless spectrum sharing where clients try to share a set of frequency bands in a distributed manner.Comment: Accepted to Sigmetrics 201
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