Characterizations of Poisson traffic streams in Jackson queueing networks

short-paper Share on Tail asymptotics of the stationary distribution for a two-node generalized Jackson network Author: Masakiyo Miyazawa Tokyo University of Science, Noda, Chiba, Japan Tokyo University of Science, Noda, Chiba, JapanView Profile Authors Info & Claims ACM SIGMETRICS Performance Evaluation ReviewVolume 42Issue 2September 2014pp 70–72https://doi.org/10.1145/2667522.2667545Published:04 September 2014Publication History 1citation26DownloadsMetricsTotal Citations1Total Downloads26Last 12 Months0Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Each feasible transition between two distinct states i and j of a continuous-time, uniform, ergodic, countable-state Markov process gives a counting process counting the number of such transitions executed by the process. Traffic processes in Markovian queueing networks can, for instance, be represented as sums of such counting processes. We prove joint functional central limit theorems for the family of counting processes generated by all feasible transitions. We characterize which weighted sums of counts have zero covariance in the limit in terms of balance equations in the transition diagram of the process. Finally, we apply our results to traffic processes in a Jackson network. In particular, we derive simple formulas for the asymptotic covariances between the processes counting the number of customers moving between pairs of nodes in such a network.

Genome-wide association studies (GWASs) seek to identify genetic variants associated with a trait, and have been a powerful approach for understanding complex diseases. A critical challenge for GWASs has been the dependence on individual-level data that typically have strict privacy requirements, creating an urgent need for methods that preserve the individual-level privacy of participants. Here, we present a privacy-preserving framework based on several advances in homomorphic encryption and demonstrate that it can perform an accurate GWAS analysis for a real dataset of more than 25,000 individuals, keeping all individual data encrypted and requiring no user interactions. Our extrapolations show that it can evaluate GWASs of 100,000 individuals and 500,000 single-nucleotide polymorphisms (SNPs) in 5.6 h on a single server node (or in 11 min on 31 server nodes running in parallel). Our performance results are more than one order of magnitude faster than prior state-of-the-art results using secure multiparty computation, which requires continuous user interactions, with the accuracy of both solutions being similar. Our homomorphic encryption advances can also be applied to other domains where large-scale statistical analyses over encrypted data are needed.

We consider cluster-based network servers in which a front-end directs incoming requests to one of a number of back-ends. Specifically, we consider content-based request distribution: the front-end uses the content requested, in addition to information about the load on the back-end nodes, to choose which back-end will handle this request. Content-based request distribution can improve locality in the back-ends' main memory caches, increase secondary storage scalability by partitioning the server's database, and provide the ability to employ back-end nodes that are specialized for certain types of requests.As a specific policy for content-based request distribution, we introduce a simple, practical strategy for locality-aware request distribution (LARD). With LARD, the front-end distributes incoming requests in a manner that achieves high locality in the back-ends' main memory caches as well as load balancing. Locality is increased by dynamically subdividing the server's working set over the back-ends. Trace-based simulation results and measurements on a prototype implementation demonstrate substantial performance improvements over state-of-the-art approaches that use only load information to distribute requests. On workloads with working sets that do not fit in a single server node's main memory cache, the achieved throughput exceeds that of the state-of-the-art approach by a factor of two to four.With content-based distribution, incoming requests must be handed off to a back-end in a manner transparent to the client, after the front-end has inspected the content of the request. To this end, we introduce an efficient TCP handoflprotocol that can hand off an established TCP connection in a client-transparent manner.

We consider cluster-based network servers in which a front-end directs incoming requests to one of a number of back-ends. Specifically, we consider content-based request distribution: the front-end uses the content requested, in addition to information about the load on the back-end nodes, to choose which back-end will handle this request. Content-based request distribution can improve locality in the back-ends’ main memory caches, increase secondary storage scalability by partitioning the server’s database, and provide the ability to employ back-end nodes that are specialized for certain types of requests. As a specific policy for content-based request distribution, we introduce a simple, practical strategy for locality-aware request distribution (LARD). With LARD, the front-end distributes incoming requests in a manner that achieves high locality in the back-ends’ main memory caches as well as load balancing. Locality is increased by dynamically subdividing the server’s working set over the back-ends. Trace-based simulation results and measurements on a prototype implementation demonstrate substantial performance improvements over state-of-the-art approaches that use only load information to distribute requests. On workloads with working sets that do not fit in a single server node’s main memory cache, the achieved throughput exceeds that of the state-of-the-art approach by a factor of two to four. With content-based distribution, incoming requests must be handed off to a back-end in a manner transparent to the client, after the front-end has inspected the content of the request. To this end, we introduce an efficient TCP handoflprotocol that can hand off an established TCP connection in a client-transparent manner.

Stochastic optimization of level-dependent perishable inventory system by Jackson network

DiffServ architecture has been widely adopted for the provision of QoS over the Internet. This makes the full understanding of its operation imperative. We believe that only mathematical analysis may have the power of such goal. As the heart of a DiffServ router is the token bucket algorithm, a generic one, with two‐colours marking, is to be considered here. A mathematical framework will be first developed for its analysis. Then, assuming an input traffic with Poisson arrivals and Exponential packet lengths, and a memoryless token bucket system, the two types of generated streams will be statistically characterized through their distributions and averages. This analysis will be carried out for two types of buckets, one with infinite size and a second with finite size. It will be shown how the derived equations will allow the prediction of the output traffic streams for given bucket and input traffic stream parameters. The paper will be then complemented by conclusions and suggestions. Copyright © 2006 John Wiley & Sons, Ltd.

Cache placement in sensor networks under an update cost constraint

In this paper, we address an optimization problem that arises in context of cache placement in sensor networks. In particular, we consider the cache placement problem where the goal is to determine a set of nodes in the network to cache/store the given data item, such that the overall communication cost incurred in accessing the item is minimized, under the constraint that the total communication cost in updating the selected caches is less than a given constant. In our network model, there is a single server (containing the original copy of the data item) and multiple client nodes (that wish to access the data item). For various settings of the problem, we design optimal, near-optimal, heuristic-based, and distributed algorithms, and evaluate their performance through simulations on randomly generated sensor networks.KeywordsSensor NetworkSensor NodeGreedy AlgorithmData ItemSteiner TreeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We introduce a Markov queueing system with Poisson arrivals, exponential services, and jockeying between two parallel and equivalent servers. An arriving customer admits to the shortest line. Every transition, of only the last customer in line, from the longer line to the shorter line may accompanied by a certain fixed cost. Thus, a transition from the longer queue to the shorter queue occurs whenever the difference between the lines reaches a certain discrete threshold (d = 2, 3, …). In this study, we focus on the stochastic analysis of the number of transitions of an arbitrary customer.

We consider an N-server queuing system with Poisson arrivals and exponential service, in which arriving customers must pass through a gate into a waiting room before becoming eligible for service. Customers who find the gate closed wait outside until the gate opens; customers inside the waiting room are served at random. When the last customer inside acquires a server, the gate admits all those outside and then closes again. If no customer is waiting outside when the gate opens, the gate remains open until there is a queue of k waiting customers. Service offered by this system is intermediary between random service and order-of-arrival service. As long as the gate is open and fewer than N + k customers are in the system, service is purely random. The parameter k can be regarded as a threshold at which the queue is judged too long to permit random service to continue. Our main results are (i) the Laplace-Stieltjes transform of the equilibrium distribution of the waiting time of an arbitrary customer and (ii) a comparison of the second moments of the waiting time for different values of k with those of the waiting time under random service and order-of-arrival service. The service is shown to be “nearly random” at low loads and “not quite order-of-arrival” at high loads; for higher values of k this transition occurs at higher traffic intensities.

Product form was first introduced by Jackson [Operations Research, 1957; Management Science, 1963] who considered only negative exponential service distributions with queue length dependent service rates. Posner and Bernholtz [Operations Research, 1968] showed that one has product form in the case where there are many classes of customers, service times are exponential with class queue length dependent service rates, and lag times (the time for a customer to travel between two servers is a random variable with continuously differentiable distribution function). Baskett, Chandy, Muntz and Palacios [JACM, 1975] extended these results to networks with multiple classes of customers and service time distributions which have rational Laplace transforms vanishing at ∞. Chandy, Howard and Towsley [JACM, 1977] extended this further to the case where the service time distribution functions are continuously differentiable. They also introduced the concept of station balance and established some important relationships between station balance, local balance and product form. In particular, for the closed queueing network they showed that if each queue in the network satisfies local balance in isolation with Poisson arrivals then one has product formsolution for the network. This paper extends previous results to arbitrary service with finite mean (the nondifferentiable case included). This is done by introducing supplementary variables for the remaining service requirements at the various queues in the system. By using generalized function (in the sense of Schwartz) a new technique is presented for handling queueing networks in which service distributions may be general.

This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let hi be the Laplace transform of the residual system sojourn time for a customer ‘arriving' to node i, ‘arrival' meaning external input or internal transfer. The transforms {hi : i = 1, ···, N} are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables {Ti : i = 1, ···, N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.

For tandem queueing networks with generally distributed service times, decomposition often is the only feasible solution method besides simulation. The network is partitioned into individual nodes which are analysed in isolation. In existing decomposition algorithms for continuous-time networks, the output of a queue is usually approximated as a renewal process, which serves as the arrival process to the next queue. In this paper, the internal traffic processes are described as semi-Markov processes (SMPs) and Markov modulated Poisson processes (MMPPs). Thus, correlations in the traffic streams, which are known to have a considerable impact on performance, are taken into account to some extent. A two-state MMPP, which arises frequently in communications modeling, serves as input to the first queue of the tandem network. For tandem networks with infinite or finite buffers, stationary mean queue lengths at arbitrary time computed quasi-promptly by the decomposition component of the tool TimeNET are compared to simulation.KeywordsQueue LengthRenewal ProcessArrival ProcessLoss ProbabilityBusy PeriodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Stochastic monotonicity properties for various classes of queueing networks have been established in the literature mainly with the use of coupling constructions. Miyazawa and Taylor (1997) introduced a class of batch-arrival, batch-service and assemble-transfer queueing networks which can be thought of as generalized Jackson networks with batch movements. We study conditions for stochastic domination within this class of networks. The proofs are based on a certain characterization of the stochastic order for continuous-time Markov chains, written in terms of their associated intensity matrices.