Heavy-Traffic Analysis of Queueing Systems with No Complete Resource Pooling

Hurtado-Lange, Daniela; Maguluri, Siva Theja

doi:10.1287/moor.2021.1248

Cited by 10 publications

(20 citation statements)

References 25 publications

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“…Define the cone K spanned by the normal to the facets [4] that, under the parametrization described above, the state space collapses into K. So, we have…”

Section: ) Heavy Traffic and Statementioning

confidence: 99%

“…Even though it provides insights on the performance of the system asymptotically, a natural question is: 'How well does the heavy traffic limiting behavior approximate the prelimit system?' Such a question can be answered by obtaining error bounds on the heavy-traffic approximation, as in [2], [3], [4]. In this paper, we obtain tight error bounds that grow logarithmically, as opposed to error bounds that grow polynomially in [2], [3], [4].…”

Section: Introductionmentioning

confidence: 97%

“…Such a question can be answered by obtaining error bounds on the heavy-traffic approximation, as in [2], [3], [4]. In this paper, we obtain tight error bounds that grow logarithmically, as opposed to error bounds that grow polynomially in [2], [3], [4].…”

Section: Introductionmentioning

confidence: 97%

“…In this paper we study a generalized switch model, which was first introduced in [5] to study several SPNs with control on the service process, such as input queued switches, ad hoc wireless networks, cloud computing, data centers etc. We consider the MaxWeight algorithm, and, using a tighter variant of the the drift argument in [2], [3], [4], we show that MaxWeight is within K 2 log 1 ǫ of the optimal policy (see Corollary 1). This is the first contribution of this paper.…”

Section: Introductionmentioning

confidence: 99%

“…We study a generalized switch without assuming that the CRP condition is satisfied, and we improve the bounds presented in [4] without adding any assumption. Specifically, we compute an upper bound of the form K 1 ǫ + K 2 log 1 ǫ for linear combinations of the queue lengths (see Theorem 1).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Logarithmic Heavy Traffic Error Bounds in Generalized Switch and Load Balancing Systems

Hurtado-Lange¹,

Varma²,

Maguluri³

2020

Preprint

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Motivated by application in wireless networks, cloud computing, data centers etc, Stochastic Processing Networks have been studied in the literature under various asymptotic regimes. In the heavy-traffic regime, the steady state mean queue length is proved to be O( 1ǫ ) where ǫ is the heavytraffic parameter, that goes to zero in the limit. The focus of this paper is on obtaining queue length bounds on prelimit systems, thus establishing the rate of convergence to the heavy traffic. In particular, we study the generalized switch model operating under the MaxWeight algorithm, and we show that the mean queue length of the prelimit system is only O log 1 ǫ away from its heavy-traffic limit. We do this even when the so called complete resource pooling (CRP) condition is not satisfied. When the CRP condition is satisfied, in addition, we show that the MaxWeight algorithm is within O log 1 ǫ of the optimal. Finally, we obtain similar results in load balancing systems operating under the join the shortest queue routing algorithm.

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“…Define the cone K spanned by the normal to the facets [4] that, under the parametrization described above, the state space collapses into K. So, we have…”

Section: ) Heavy Traffic and Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Logarithmic Heavy Traffic Error Bounds in Generalized Switch and Load Balancing Systems

Hurtado-Lange¹,

Varma²,

Maguluri³

2020

Preprint

Self Cite

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A Mathematical Model for Cloud-Based Scheduling Using Heavy Traffic Limit Theorem in Queuing Process

Rashidifar

Chen

Bouzary

et al. 2022

Lecture Notes in Mechanical Engineering

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Cloud manufacturing (CMfg) is a service-oriented manufacturing paradigm that distributes resources in an on-demand business model. In the cloud manufacturing environment, scheduling is considered as an effective tool for satisfying customer requirements which has attracted attention from researchers. In this case, quality of service (QoS) in the scheduling plays a vital role in assessing the impacts of the distributed resources in operation on the performance of scheduling functions. In this paper, a queuing system is employed to model the scheduling problem with multiple servers and then scheduling in cloud manufacturing is classified based on various QoS requirements. Moreover, a set of heavy traffic limit theorems is introduced as a new approach to solving this scheduling problem in which different heavy traffic limits are provided for each of QoS-based scheduling classes. Finally, the number of operational resources in the scheduling is determined by considering the results obtained in the numerical analysis of the heavy traffic limit with different queue disciplines. The results show that different numbers of active machines in various QoS requirements classes play a vital role in that the required QoS metrics such as the expected waiting time and the expected completion time which are critical performance indicators of the cloud’s service are intimately related.

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Heavy traffic analysis of multi-class bipartite queueing systems under FCFS

Hillas,

Caldentey,

Gupta

2024

Queueing Syst

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This paper examines the performance of multi-class, multi-server bipartite queueing systems, where each arriving customer is compatible with only a subset of servers. We focus on the system’s performance under a first-come, first-served-assign longest idle server service discipline. In this discipline, an idle server is matched with the compatible customer who has been waiting the longest, and a customer who can be served by multiple idle servers is routed to the server that has been idle for the longest period. We analyse the system under conventional heavy-traffic conditions, where the traffic intensity approaches one from below. Building upon the formulation and results of Afèche et al. (Oper Res 70(1):363–401, 2022), we generalize the model by allowing the vector of arrival rates to approach the heavy-traffic limit from an arbitrary direction. We characterize the steady-state waiting times of the various customer classes and demonstrate that a much wider range of waiting time outcomes is achievable. Furthermore, we establish that the matching probabilities, i.e. the probabilities of different customer classes being served by different servers, do not depend on the direction along which the system approaches heavy traffic. We also investigate the design of compatibility between customer classes and servers, finding that a service provider who has complete control over the matching can design a delay-minimizing matching by considering only the limiting arrival rates. When some constraints on the compatibility structure exist, the direction of convergence to heavy-traffic affects which compatibility structure minimizes delay. Additionally, we discover that the bipartite matching queueing system exhibits a form of Braess’s paradox, where adding more connectivity to an existing system can lead to higher average waiting times, despite the fact that neither customers nor servers act strategically.

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Heavy-Traffic Analysis of Queueing Systems with No Complete Resource Pooling

Cited by 10 publications

References 25 publications

Logarithmic Heavy Traffic Error Bounds in Generalized Switch and Load Balancing Systems

Logarithmic Heavy Traffic Error Bounds in Generalized Switch and Load Balancing Systems

A Mathematical Model for Cloud-Based Scheduling Using Heavy Traffic Limit Theorem in Queuing Process

Heavy traffic analysis of multi-class bipartite queueing systems under FCFS

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