Performance analysis of queueing systems with resequencing

2014 - 2015The service sector lies at the heart of industrialized nations and continues to serve as a major contributor to the world economy. Over the years, the service industry has given rise to an enor- mous amount of technological, scienti c, and managerial chal- lenges. Among all challenges, operational service quality, service efficiency, and the tradeoffs between the two have always been at the center of service managers' attention and are likely to be so more in the future. Queueing theory attempts to address these challenges from a mathematical perspective. Every service station of a queueing network is characterized by two major components: the external arrival process and the service process. The external arrival process governs the timing of service request arrivals to that station from outside, and the service process concerns the duration of service transactions in that station... [edited by author]XIV n.s

Estimation of Network Disordering Eff ects by In-depth Analysis of the Resequencing Bu ffer Contents in Steady-state, Journal of Telecommunications and Information Technology, 2016, nr 1

The paper is devoted to the analytic analysis of resequencing issue, which is common in packet networks, using queueing-theoretic approach. The authors propose the mathematical model, which describes the simplest setting of packet resequencing, but which allows one to make the first step in the in-depth-analysis of the queues dynamics in the resequencing buffer. Specifically consideration is given to N-server queueing system (N > 3) with single infinite capacity buffer and resequencing, which may serve as a model of packet reordering in packet networks. Customers arrive at the system according to Poisson flow, occupy one place in the buffer and receive service from one of the servers, which is exponentially distributed with the same parameter. The order of customers upon arrival has to be preserved upon departure. Customers, which violated the order are kept in resequencing buffer which also has infinite capacity. It is shown that the resequencing buffer can be considered as consisting of n, 1 ≤ n ≤ N −1, interconnected queues, depending on the number of busy servers, with i-th queue containing customers, which have to wait for i service completions before they can leave the system. Recursive algorithm for computation of the joint stationary distribution of the number of customers in the buffer and servers, and each queue in resequencing buffer are being obtained. Numerical examples, which show the dynamics of the characteristics of the queues in resequencing buffer are given

Computable bounds in fork-join queueing systems

In a Fork-Join (FJ) queueing system an upstream fork station splits incoming jobs into N tasks to be further processed by N parallel servers, each with its own queue; the response time of one job is determined, at a downstream join station, by the maximum of the corresponding tasks' response times. This queueing system is useful to the modelling of multi-service systems subject to synchronization constraints, such as MapReduce clusters or multipath routing. Despite their apparent simplicity, FJ systems are hard to analyze. This paper provides the first computable stochastic bounds on the waiting and response time distributions in FJ systems. We consider four practical scenarios by combining 1a) renewal and 1b) non-renewal arrivals, and 2a) non-blocking and 2b) blocking servers. In the case of non blocking servers we prove that delays scale as O(logN), a law which is known for first moments under renewal input only. In the case of blocking servers, we prove that the same factor of log N dictates the stability region of the system. Simulation results indicate that our bounds are tight, especially at high utilizations, in all four scenarios. A remarkable insight gained from our results is that, at moderate to high utilizations, multipath routing 'makes sense' from a queueing perspective for two paths only, i.e., response times drop the most when N = 2; the technical explanation is that the resequencing (delay) price starts to quickly dominate the tempting gain due to multipath transmissions

Stochastic bounds in fork-join queueing systems under full and partial mapping

In a Fork-Join (FJ) queueing system an upstream fork station splits incoming jobs into N tasks to be further processed by N parallel servers, each with its own queue; the response time of one job is determined, at a downstream join station, by the maximum of the corresponding tasks’ response times. This queueing system is useful to the modelling of multi-service systems subject to synchronization constraints, such as MapReduce clusters or multipath routing. Despite their apparent simplicity, FJ systems are hard to analyze. This paper provides the first computable stochastic bounds on the waiting and response time distributions in FJ systems under full (bijective) and partial (injective) mapping of tasks to servers. We consider four practical scenarios by combining 1a) renewal and 1b) non-renewal arrivals, and 2a) non-blocking and 2b) blocking servers. In the case of non-blocking servers we prove that delays scale as O(log N), a law which is known for first moments under renewal input only. In the case of blocking servers, we prove that the same factor of log N dictates the stability region of the system. Simulation results indicate that our bounds are tight, especially at high utilizations, in all four scenarios. A remarkable insight gained from our results is that, at moderate to high utilizations, multipath routing “makes sense” from a queueing perspective for two paths only, i.e., response times drop the most when N = 2; the technical explanation is that the resequencing (delay) price starts to quickly dominate the tempting gain due to multipath transmissions

Resequencing delays under multipath routing -- Asymptotics in a simple queueing model

We study the resequencing delay caused by multipath routing. We use a queueing model which consists of parallel queues to model the network routing behavior. We define a new metric denoted by $gamma$, to study the impact of resequencing on the customer end-to-end delay. Our results characterize some properties of $gamma$ with respect to different service time distributions. In particular, the resequencing delay can be negligible when the delay along each path is light-tailed, but can be of major concern when it is heavy-tailed

Performance Modelling and Optimisation of Multi-hop Networks

A major challenge in the design of large-scale networks is to predict and optimise the total time and energy consumption required to deliver a packet from a source node to a destination node. Examples of such complex networks include wireless ad hoc and sensor networks which need to deal with the effects of node mobility, routing inaccuracies, higher packet loss rates, limited or time-varying effective bandwidth, energy constraints, and the computational limitations of the nodes. They also include more reliable communication environments, such as wired networks, that are susceptible to random failures, security threats and malicious behaviours which compromise their quality of service (QoS) guarantees. In such networks, packets traverse a number of hops that cannot be determined in advance and encounter non-homogeneous network conditions that have been largely ignored in the literature. This thesis examines analytical properties of packet travel in large networks and investigates the implications of some packet coding techniques on both QoS and resource utilisation. Specifically, we use a mixed jump and diffusion model to represent packet traversal through large networks. The model accounts for network non-homogeneity regarding routing and the loss rate that a packet experiences as it passes successive segments of a source to destination route. A mixed analytical-numerical method is developed to compute the average packet travel time and the energy it consumes. The model is able to capture the effects of increased loss rate in areas remote from the source and destination, variable rate of advancement towards destination over the route, as well as of defending against malicious packets within a certain distance from the destination. We then consider sending multiple coded packets that follow independent paths to the destination node so as to mitigate the effects of losses and routing inaccuracies. We study a homogeneous medium and obtain the time-dependent properties of the packet’s travel process, allowing us to compare the merits and limitations of coding, both in terms of delivery times and energy efficiency. Finally, we propose models that can assist in the analysis and optimisation of the performance of inter-flow network coding (NC). We analyse two queueing models for a router that carries out NC, in addition to its standard packet routing function. The approach is extended to the study of multiple hops, which leads to an optimisation problem that characterises the optimal time that packets should be held back in a router, waiting for coding opportunities to arise, so that the total packet end-to-end delay is minimised

Delivering Consistent Network Performance in Multi-tenant Data Centers

Data centers are growing rapidly in size and have recently begun acquiring a new role as cloud hosting platforms, allowing outside developers to deploy their own applications on large scales. As a result, today\u27s data centers are multi-tenant environments that host an increasingly diverse set of applications, many of which have very demanding networking requirements. This has prompted research into new data center architectures that offer increased capacity by using topologies that introduce multiple paths between servers. To achieve consistent network performance in these networks, traffic must be effectively load balanced among the available paths. In addition, some form of system-wide traffic regulation is necessary to provide performance guarantees to tenants. To address these issues, this thesis introduces several software-based mechanisms that were inspired by techniques used to regulate traffic in the interconnects of scalable Internet routers. In particular, we borrow two key concepts that serve as the basis for our approach. First, we investigate packet-level routing techniques that are similar to those used to balance load effectively in routers. This work is novel in the data center context because most existing approaches route traffic at the level of flows to prevent their packets from arriving out-of-order. We show that routing at the packet-level allows for far more efficient use of the network\u27s resources and we provide a novel resequencing scheme to deal with out-of-order arrivals. Secondly, we introduce distributed scheduling as a means to engineer traffic in data centers. In routers, distributed scheduling controls the rates between ports on different line cards enabling traffic to move efficiently through the interconnect. We apply the same basic idea to schedule rates between servers in the data center. We show that scheduling can prevent congestion from occurring and can be used as a flexible mechanism to support network performance guarantees for tenants. In contrast to previous work, which relied on centralized controllers to schedule traffic, our approach is fully distributed and we provide a novel distributed algorithm to control rates. In addition, we introduce an optimization problem called backlog scheduling to study scheduling strategies that facilitate more efficient application execution

JTIT

kwartalni

BMSN and SpiderNet as large scale ATM switch interconnection architectures.

by Kin-Yu Cheung.Thesis (M.Phil.)--Chinese University of Hong Kong, 1997.Includes bibliographical references (leaves 64-[68]).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Multistage Interconnection Architectures --- p.2Chapter 1.2 --- Interconnection Topologies --- p.4Chapter 1.3 --- Design of Switch Module-An Example of Multichannel Switch --- p.7Chapter 1.4 --- Organization --- p.8Chapter 1.5 --- Publication --- p.9Chapter 2 --- BMSN and SpiderNet: Two Large Scale ATM Switches --- p.13Chapter 2.1 --- Introduction --- p.13Chapter 2.2 --- Architecture --- p.14Chapter 2.2.1 --- Topology --- p.14Chapter 2.2.2 --- Switch Modules --- p.15Chapter 2.3 --- Routing --- p.17Chapter 2.3.1 --- VP/VC Routing --- p.18Chapter 2.3.2 --- VP/VC Routing Control --- p.22Chapter 2.3.3 --- Cell Routing --- p.23Chapter 2.3.4 --- Alternate Path Routing for Fault Tolerance --- p.24Chapter 2.4 --- SpiderNet --- p.25Chapter 2.5 --- Performance and Discussion --- p.26Chapter 2.5.1 --- BMSN vs SpiderNet --- p.26Chapter 2.5.2 --- Network Capacity --- p.29Chapter 2.6 --- Concluding Remarks --- p.30Chapter 3 --- Multichannel ATM Switching --- p.39Chapter 3.1 --- Introduction --- p.39Chapter 3.2 --- Switch Design --- p.40Chapter 3.3 --- Channel Allocation Algorithms --- p.41Chapter 3.3.1 --- VC-Based String Round Robin (VCB-SRR) Algorithm --- p.41Chapter 3.3.2 --- Implementation of the VCB-SRR Algorithm --- p.43Chapter 3.3.3 --- Channel Group Based Round Robin (CGB-RR) Algorithm --- p.50Chapter 3.3.4 --- Implementation of the CGB-RR Algorithm --- p.51Chapter 3.4 --- Performance and Discussion --- p.53Chapter 3.5 --- Concluding Remarks --- p.57Chapter 4 --- Conclusion --- p.62Bibliography --- p.6