Scalable Load Balancing in Networked Systems: Universality Properties and Stochastic Coupling Methods

Boor, Mark van der; Borst, Sem; Leeuwaarden, Johan S. H. van; Mukherjee, Debankur

doi:10.48550/arxiv.1712.08555

Cited by 3 publications

(4 citation statements)

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“…Such schemes improve the system's performance by dividing the work effectively among the participating nodes. Under certain conditions (identical servers, exponential service times, and service protocols that do not depend on the service requirement, such as the FCFS), the so-called join the shortest queue (JSQ) policy has several strong optimality properties: The JSQ policy minimises the overall mean delay among the class of load balancing policies that do not have any advance knowledge of the service requirements [19,40,60].…”

Section: Related Workmentioning

confidence: 99%

“…The employed cooperation strategy among source and relays is queue-based, with as ultimate goal to minimise the total transmission time, i.e., the time that is needed to transmit a packet from the source to the destination. To this end, we consider join the shortest queue policy as it seems to be the most appropriate for such a wireless network [39,40,60,63].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the shortest relay queue policy in a cooperative random access network with collisions

2019

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The scope of this work is twofold: On the one hand, strongly motivated by emerging engineering issues in multiple access communication systems, we investigate the performance of a slotted-time relay-assisted cooperative random access wireless network with collisions and with join the shortest queue relay-routing protocol. For this model, we investigate the stability condition, and apply different methods to derive the joint equilibrium distribution of the queue lengths. On the other hand, using the cooperative communication system as a vehicle for illustration, we investigate and compare three different approaches for this type of multi-dimensional stochastic processes, namely the compensation approach, the power series algorithm (PSA), and the probability generating function (PGF) approach. We present an extensive numerical comparison of the compensation approach and PSA, and discuss which method performs better in terms of accuracy and computation time. We also provide details on how to compute the PGF in terms of a solution of a Riemann-Hilbert boundary value problem.Cooperative communication is a new communication paradigm in which different terminals (i.e., nodes, devices) in a wireless network share their antennas and resources for distributed transmission and processing. Recent studies have shown that cooperative communications yield significant performance improvements for 5G networks, which need massive uncoordinated access, low latency, energy efficiency and ultra-reliability [45].The unprecedented growth of wireless networking, and the ever growing demand for higher data rates and capacity over the last decades, have already pushed the limits of current cellular systems [57]. By exploiting the spatial diversity inherent to wireless channels, which is an important tool to overcome the effects of fading (decrease in signal power due to path loss), shadowing and attenuation (decrease in signal strength), relay-based cooperative communications have been proposed as the appropriate solution to achieve the requirements of future needs; see e.g., [31,37]. * m.mayank@tue.nl † idimit@math.upatras.gr ‡ s.kapodistria@tue.nl arXiv:1810.00754v1 [math.PR] 1 Oct 2018 ContributionApplication oriented contribution. In this work, we consider a slotted-time relay-assisted cooperative communication system with a JSQ routing protocol at the relays and collisions. Such models have not been extensively analysed and very little is known regarding their delay performance. In particular, we provide insights on the characterisation of the delay and the performance of the system at hand. This is a particularly difficult task even in small scale systems, due to the strong interdependence/interaction between the queues. Furthermore, we demonstrate how to obtain the equilibrium distribution of the joint queue lengths and present an extensive numerical comparison of the techniques implemented, discussing which performs better in terms of accuracy and time complexity (computational time).

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of the shortest relay queue policy in a cooperative random access network with collisions

2019

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“…The JIQ policy only has a constant communication overhead per job, but requires memory at the dispatcher. We refer to Van der Boor et al [21] and Gamarnik et al [6] for further details.…”

Section: Introductionmentioning

confidence: 99%

Job assignment in large-scale service systems with affinity relations

2019

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We consider load balancing in service systems with affinity relations between jobs and servers. Specifically, an arriving job can be allocated to a fast, primary server from a particular selection associated with this job or to a secondary server to be processed at a slower rate. Such job-server affinity relations can model network topologies based on geographical proximity, or data locality in cloud scenarios. We introduce load balancing schemes that allocate jobs to primary servers if available, and otherwise to secondary servers. A novel coupling construction is developed to obtain stability conditions and performance bounds using a coupling technique. We also conduct a fluid limit analysis for symmetric model instances, which reveals a delicate interplay between the model parameters and load balancing performance.

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“…This seminal work has led to several significant developments: (i) [3] proved that the stationary distribution indeed converges to the stationary distribution of the two-dimensional diffusion limit based on Stein's method; and (ii) via stochastic coupling, [13] showed that the diffusion limit of Pod converges to that of JSQ in the Halfin-Whitt regime at the process level (over finite time) when d = Θ( √ N log N); and (iii) when α < 1/6, [10] proved that the waiting probability of a job is asymptotically zero with d = ω 1 1−λ at the steady-state based on Stein's method. Interested readers can find a comprehensive survey of recent results in [16].…”

Section: Introductionmentioning

confidence: 99%

A Simple Steady-State Analysis of Load Balancing Algorithms in the Sub-Halfin-Whitt Regime

Liu

Lü

2019

SIGMETRICS Perform. Eval. Rev.

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I. abstractThis paper studies a class of load balancing algorithms for many-server (N servers) systems assuming finite buffer with size b − 1 (i.e. a server can have at most one job in service and b − 1 jobs in queue). We focus on steady-state performance of load balancing algorithms in the heavy traffic regime such that the load of system is λ = 1 − N −α for 0 < α < 0.5, which we call sub-Halfin-Whitt regime (α = 0.5 is the so-called the Halfin-Whitt regime). We establish a sufficient condition under which the probability that an incoming job is routed to an idle server is one asymptotically. The class of load balancing algorithms that satisfy the condition includes join-the-shortest-queue (JSQ), idle-one-first (I1F), join-the-idle-queue (JIQ), and powerof-d-choices (Pod) with d = N α log N. The proof of the main result is based on the framework of Stein's method. A key contribution is to use a simple generator approximation based on state space collapse.

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Scalable Load Balancing in Networked Systems: Universality Properties and Stochastic Coupling Methods

Cited by 3 publications

References 0 publications

Analysis of the shortest relay queue policy in a cooperative random access network with collisions

Analysis of the shortest relay queue policy in a cooperative random access network with collisions

Job assignment in large-scale service systems with affinity relations

A Simple Steady-State Analysis of Load Balancing Algorithms in the Sub-Halfin-Whitt Regime

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