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

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

Open queueing networks : optimization and performance evaluation models for discrete manufacturing systems

Includes bibliographical references (p. 41-45).Research supported by Fundac̦ão de Amparo a Pesquisa do Estado de São Paulo, Brazil.by Gabriel R. Bitran, Reinaldo Morabito

A STUDY OF QUEUING THEORY IN LOW TO HIGH REWORK ENVIRONMENTS WITH PROCESS AVAILABILITY

In manufacturing systems subject to machine and operator resource constraints the effects of rework can be profound. High levels of rework burden the resources unnecessarily and as the utilization of these resources increases the expected queuing time of work in process increases exponentially. Queuing models can help managers to understand and control the effects of rework, but often this tool is overlooked in part because of concerns over accuracy in complex environments and/or the need for limiting assumptions. One aim of this work is to increase understanding of system variables on the accuracy of simple queuing models. A queuing model is proposed that combines G/G/1 modeling techniques for rework with effective processing time techniques for machine availability and the accuracy of this model is tested under varying levels of rework, external arrival variability, and machine availability. Results show that the model performs best under exponential arrival patterns and can perform well even under high rework conditions. Generalizations are made with regards to the use of this tool for allocation of jobs to specific workers and/or machines based on known rework rates with the ultimate aim of queue time minimization

A Specific Network Link and Path Likelihood Prediction Tool

Communications have always been a crucial part of any military operation. As the pace of warfare and the technological complexity of weaponry have increased, so has the need for rapid information to assess battlefield conditions. Message passing across a network of communication nodes allowed commanders to communicate with their forces. It is clear that an accurate prediction of communication usage through a network will provide commanders with useful intelligence of friendly and unfriendly activities. Providing a specific network link and path likelihood prediction tool gives strategic military commanders additional intelligence information and enables them to manage their limited resources more efficiently. In this study, Dijkstra\u27s algorithm has been modified to allow the Queueing Network Analyzer\u27s (QNA) analysis output to act as a node\u27s goodness metric. QNA\u27s calculation of the expected Total Sojourn Time for the completion of queueing and service in a node provides accurate measurement of expected congestion. The modified Dijkstra\u27s algorithm in the Generalized Network Analyzer (GNA) is verified and empirically validated to properly deliver traffic. It appropriately generates the fastest traffic path from a start node to a destination node. This implementation includes notification if input parameters exceed the network\u27s processing capability. GNA\u27s Congestion Control displays notification and informs the user certain network input parameters must be lowered (PTR or BSTR) or where certain nodes must be improved to maintain node stability. With this unstable node identification, users can determine which node needs attention and improvements. Once this instability is removed, a good QoS is achieved and analysis proceeds

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"

Decomposition of general queueing network models. An investigation into the implementation of hierarchical decomposition schemes of general closed queueing network models using the principle of minimum relative entropy subject to fully decomposable constraints.

Decomposition methods based on the hierarchical partitioning of the state space of queueing network models offer powerful evaluation tools for the performance analysis of computer systems and communication networks. These methods being conventionally implemented capture the exact solution of separable queueing network models but their credibility differs when applied to general queueing networks. This thesis provides a universal information theoretic framework for the implementation of hierarchical decomposition schemes, based on the principle of minimum relative entropy given fully decomposable subset and aggregate utilization, mean queue length and flow-balance constraints. This principle is used, in conjuction with asymptotic connections to infinite capacity queues, to derive new closed form approximations for the conditional and marginal state probabilities of general queueing network models. The minimum relative entropy solutions are implemented iteratively at each decomposition level involving the generalized exponential (GE) distributional model in approximating the general service and asymptotic flow processes in the network. It is shown that the minimum relative entropy joint state probability, subject to mean queue length and flow-balance constraints, is identical to the exact product-form solution obtained as if the network was separable. An investigation into the effect of different couplings of the resource units on the relative accuracy of the approximation is carried out, based on an extensive experimentation. The credibility of the method is demonstrated with some illustrative examples involving first-come-first-served general queueing networks with single and multiple servers and favourable comparisons against exact solutions and other approximations are made

Timestep Stochastic Simulation of Computer Networks using Diffusion Approximation

Performance evaluation of modern computer networks is challenging because of their large sizes, high speeds of communication links, and complex state-dependent control mechanisms. In particular, TCP congestion control reacts in a nonlinear fashion to the state of the network at the time scale of round-trip times, making analysis intractable. Thus packet-level simulation is the only widely used method of performance evaluation. Although it can be accurate, it is computationally expensive and thus can be applied only to small networks and low link speeds. Timestep Stochastic Simulation (TSS) is a novel method for generating sample paths of computer networks, in increments of time steps rather than packet transmissions. TSS has a low computation cost independent of packet rates and provides adequate accuracy for evaluating general state-dependent control mechanisms. TSS generates the evolution of the system state S(t) on a sample path in time steps of size delta. At each step, S(t + delta) is randomly chosen according to S(t) and the probability distribution Pr[S(t+delta)|S(t)], obtained using the diffusion approximation. Because packet transmission and reception events are replaced by time steps, TSS generates sample paths at a fraction of the cost of packet-level simulation. Because TSS generates sample paths, it can accurately model state-dependent control mechanisms, including TCP congestion control, adaptive dynamic routing, and so on. We have a TSS implementation for general computer networks with state-dependent control. We have applied this to numerous networks with TCP and state-dependent UDP flows, and confirmed its accuracy against packet-level simulation