Job assignment in large-scale service systems with affinity relations

Cardinaels, Ellen; Borst, Sem; Leeuwaarden, Johan S. H. van

doi:10.1007/s11134-019-09633-y

Cited by 9 publications

(10 citation statements)

References 63 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The positive Harris recurrence from part (i) of Theorem 4.8 follows from known techniques in [3] or [6]. However, as we prove the tightness in part (ii), the positive recurrence follows as a side result.…”

Section: Stability and Tightnessmentioning

confidence: 82%

“…More recently, Cardinaels et al [6] analyze stability conditions and obtain performance bounds of a general model for load balancing with affinity relations. In this setup, each arriving task can be routed to either a fast, primary selection of servers or a secondary selection with a slower processing speed.…”

Section: Related Workmentioning

confidence: 99%

“…As mentioned in the introduction, Bramson [3] and more recently, Cardinaels et al [6] analyzed the stability of JSQ-type policies in a related framework. The subcriticality condition (3.2) is equivalent to the those stated in [3,6], although our condition is stated for a sequence of graphs, later to be used for tightness of the steady state occupancy process, and the latter conditions are stated for a fixed system. As noted in [3, page 1571], the subcriticality condition as stated in Definition 3.3, is also a necessary condition for stability.…”

Section: Remarkmentioning

confidence: 99%

See 2 more Smart Citations

Load Balancing Under Strict Compatibility Constraints

Rutten¹,

Mukherjee²

2020

Preprint

View full text Add to dashboard Cite

We study large-scale systems operating under the JSQ(d) policy in the presence of stringent task-server compatibility constraints. Consider a system with N identical single-server queues and M(N) task types, where each server is able to process only a small subset of possible task types. Each arriving task selects d ≥ 2 random servers compatible to its type, and joins the shortest queue among them. The compatibility constraint is naturally captured by a fixed bipartite graph G N between the servers and the task types. When G N is complete bipartite, the meanfield approximation is proven to be accurate. However, such dense compatibility graphs are infeasible due to their overwhelming implementation cost and prohibitive storage capacity requirement at the servers. Our goal in this paper is to characterize the class of sparse compatibility graphs for which the meanfield approximation remains valid.To achieve this, first, we introduce a novel graph expansion-based notion, called proportional sparsity, and establish that systems with proportionally sparse compatibility graphs match the performance of a fully flexible system, asymptotically in the large-system limit. Furthermore, for any c(N) satisfyingas N → ∞, we show that proportionally sparse random compatibility graphs can be designed, so that the degree of each server is at most c(N). This reduces the serverdegree almost by a factor N/ ln(N), compared to the complete bipartite compatibility graph, while maintaining the same asymptotic performance. Extensive simulation experiments are conducted to corroborate the theoretical results.

show abstract

Section: Stability and Tightnessmentioning

confidence: 82%

Section: Related Workmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

Load Balancing Under Strict Compatibility Constraints

Rutten¹,

Mukherjee²

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…For an accurate performance assessment, it is however essential that the stochastic characteristics of the production processes and of the demand are accurately estimated. The statistical inference of the model parameters can either be based on prior measurements or can be learned while the production system is running using an exploration-exploitation approach [40,41], and this will be considered in future work.…”

Section: Discussionmentioning

confidence: 99%

Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production

et al. 2020

View full text Add to dashboard Cite

We present a comprehensive numerical approach with reasonably light complexity in terms of implementation and computation for assessing the performance of hybrid make-to-stock (MTS)/make-to-order (MTO) systems. In such hybrid systems, semi-finished products are produced up front and stored in a decoupling inventory. When an order arrives, the products are completed and possibly customised. We study this system in a stochastic setting: demand and production are modelled by random processes. In particular, our model includes two coupled Markovian queues: one queue represents the decoupling inventory and the other the order backlog. These queues are coupled as order processing can only occur when both queues are non-empty. We rely on matrix analytic techniques to study the performance of the MTO/MTS system under non-restrictive stochastic assumptions. In particular, we allow for arrival correlation and non-exponential setup and MTS and MTO processing times, while the hybrid MTS/MTO system is managed by an (s,S)-type threshold policy that governs switching from MTO to MTS and back. By some numerical examples, we assess the impact of inventory control, irregular order arrivals, setup and order processing times on inventory levels and lead times.

show abstract

“…Our bipartite graph model also resembles other problems in the literature. One particular model is the job-server affinity model for data locality problems studied in [9,51,52,47]. In the job-server affinity model, if one job is served by a server with its data, it has a fast constant service rate.…”

Section: … …mentioning

confidence: 99%

Optimal Load Balancing in Bipartite Graphs

Weng,

Zhou,

Srikant

2020

Preprint

View full text Add to dashboard Cite

Applications in cloud platforms motivate the study of efficient load balancing under job-server constraints and server heterogeneity. In this paper, we study load balancing on a bipartite graph where left nodes correspond to job types and right nodes correspond to servers, with each edge indicating that a job type can be served by a server. Thus edges represent locality constraints, i.e., each job can only be served at servers which contained certain data and/or machine learning (ML) models. Servers in this system can have heterogeneous service rates. In this setting, we investigate the performance of two policies named Join-the-Fastest-of-the-Shortest-Queue (JFSQ) and Join-the-Fastest-of-the-Idle-Queue (JFIQ), which are simple variants of Join-the-Shortest-Queue and Jointhe-Idle-Queue, where ties are broken in favor of the fastest servers. Under a "well-connected" graph condition, we show that JFSQ and JFIQ are asymptotically optimal in the mean response time when the number of servers goes to infinity. In addition to asymptotic optimality, we also obtain upper bounds on the mean response time for finite-size systems. We further show that the wellconnectedness condition can be satisfied by a random bipartite graph construction with relatively sparse connectivity. However, the above classical load balancing model may not be appropriate for certain modern cloud computing and data analytic applications due to the presence of job-server constraints. Under such constraints, a job can only be dispatched to a subset of the N servers. These constraints, often called locality constraints, are quite common in large-scale Machine Learning as a Service (MLaaS) and serverless computing services supported by cloud computing

show abstract

Job assignment in large-scale service systems with affinity relations

Cited by 9 publications

References 63 publications

Load Balancing Under Strict Compatibility Constraints

Load Balancing Under Strict Compatibility Constraints

Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production

Optimal Load Balancing in Bipartite Graphs

Contact Info

Product

Resources

About