Predicting departure times in multi-stage queueing systems

We develop an approximation model for the state-dependent sojourn time distribution of customers or orders in a multi-stage, multi-server queueing system, when interarrival and service times can take on general distributions. The model can be used to make probabilistic statements about the departure time of a customer or order, given the number and location of customers currently in process or waiting, and these probabilities can be recomputed while waiting at any point during the sojourn time. The model uses phase-type distributions and a new method to estimate the remaining processing times of customers in service when the sojourn time distribution is computed.     

The scale factor: a new degree of freedom in phase-type approximation

This paper introduces a unified approach to phase-type approximation in which the discrete and the continuous phase-type models form a common model set. The models of this common set are assigned with a non-negative real parameter, the scale factor. The case when the scale factor is strictly positive results in discrete phase-type distributions and the scale factor represents the time elapsed in one step. If the scale factor is 0, the resulting class is the class of CPH distributions. Applying the above view, it is shown that there is no qualitative difference between the discrete and the CPH models. Based on this unified view of phase-type models one can choose the best phase-type approximation of a stochastic model by optimizing the scale factor.     

Sensitivity analysis of distributed parameter elements in high-speed circuit networks

This paper presents an analysis method, based on MacCormack＇s technique, for the evaluation of the time domain sensitivity of distributed parameter elements in high-speed circuit networks. Sensitivities can be calculated from electrical and physical parameters of the distributed parameter elements. The proposed method is a direct numerical method of time-space discretization and does not require complicated mathematical deductive process. Therefore, it is very convenient to program this method. It can be applied to sensitivity analysis of general transmission lines in linear or nonlinear circuit networks. The proposed method is second-order-accurate. Numerical experiment is presented to demonstrate its accuracy and efficiency.     

Waiting time distribution in a class of discrete-time cyclic service multi-queue systems

A new approximate method is developed for finding the waiting and sojourn time distributions in a class of multi-queue systems served in cyclic order at discrete intervals. An immediate application for such a model is in communication networks where a number of different traffic sources compete to access a group of transmission channels operating under a time-slotted sharing policy. This system maps naturally onto a model in which the inter-visit time has a probability mass function of phase-type. We derive a set of matrix equations with easily tractable iterative procedures for their solution and controllable accuracy in their numerical evaluation. We then validate the analytical model against simulation and discuss the validity of the assumptions. This methodology can be extended to several other polling strategies.     

Analysis of threshold-based batch-service queueing systems with batch arrivals and general service times

Most research concerning batch-service queueing systems has focussed on some specific aspect of the buffer content. Further, the customer delay has only been examined in the case of single arrivals. In this paper, we examine three facets of a threshold-based batch-service system with batch arrivals and general service times. First, we compute a fundamental formula from which an entire gamut of known as well as new results regarding the buffer content of batch-service queues can be extracted. Second, we produce accurate light- and heavy-traffic approximations for the buffer content. Third, we calculate various quantities with regard to the customer delay. This paper thus provides a whole spectrum of tools to evaluate the performance of batch-service systems.     

Mean message waiting times in symmetric multi-queue systems with cyclic service

A new performance analysis is provided for a cyclic service system consisting of statistically identical stations where at most one message is served for any station in a cycle. We assume that the time is slotted and that the number of message arrivals at each station in any slot is independent and generally distributed. The switch-over time and message service time (integral multiples of the slot size) are also generally distributed. For this system (called limited service system) we find the mean message waiting time explicitly. In the case of Poisson arrivals we show that our mean message waiting time is greater than that for the gated service system which is greater than that for the exhaustive service system. We also summarize the corresponding results for the three types of services in continuous-time systems.     

The distribution of network states during residence times in product form queueing networks

Product form queueing networks are so named because their equilibrium state probabilities have a simple product form. This simple form has lead to computationally efficient techniques for obtaining solutions of these networks. Recent work on the probability of network states at those instants when a customer completes service at a service center (departure instants) or arrives at a service center (arrival instants) has revealed a similar product form. The arrival instant result provides a simple, intuitive explanation of the Mean Value Analysis solution technique for product form networks with First-Come-First-Served service centers.In this paper we derive the distribution of network states seen by a particular customer while resident at a particular service center. This distribution too has a relatively simple product form. We use this information to explain in an intuitive way the MVA solution technique for a more general class of network, those containing load independent Processor Sharing and last-Come-First-Served-Preemptive-Resume service centers. It is hoped that, just as the intuitive explanation of the response time formula for FCFS centers has led to approximation techniques for non-separable FCFS centers, this new information may provide approximation techniques for non-separable centers with other scheduling disciplines such as preemptive and non-preemptive priority.     

Tail probabilities of the delay in a batch-service queueing model with batch-size dependent service times and a timer mechanism

We deduce approximations for the tail probabilities of the customer delay in a discrete-time queueing model with batch arrivals and batch service. As in telecommunications systems transmission times are dependent on packet sizes, we consider a general dependency between the service time of a batch and the number of customers within it. The model also incorporates a timer mechanism to avoid excessive delays stemming from the requirement that a service can only be initiated when the number of present customers reaches or exceeds a service threshold. The service discipline is first-come, first-served (FCFS). We demonstrate in detail that our approximations are very useful for the purpose of assessing the order of magnitude of the tail probabilities of the customer delay, except in some special cases that we discuss extensively. We also illustrate that neglecting batch-size dependent service times or a timer mechanism can lead to a devastating assessment of the tail probabilities of the customer delay, which highlights the necessity to include these features in the model. The results from this paper can, for instance, be applied to assess the quality of service (QoS) of Voice over IP (VoIP) conversations, which is typically expressed in terms of the order of magnitude of the probability of packet loss due to excessive delays.     

Discriminatory processor sharing queues with stationary ergodic service times and the performance of TCP in overload

In a recent paper, Bonald and Roberts (2001) [6] studied non-persistent TCP connections in transient overload conditions, under the assumption that all connections have the same round-trip times. In this paper our goal is to develop theoretical tools that will enable us to relax this assumption and obtain explicit expressions for the rate of growth of the number of connections at the system, the rate at which TCP connections leave the system, as well as the time needed for the completion of a connection. To that end, we model the system as a discriminatory processor sharing (DPS) system which we analyze under very mild assumptions on the probability distributions related to different classes of arrivals: we only assume that the arrival rates of connections exist, and that the amount of information transmitted during a connection of a given type forms a stationary ergodic sequence. We then proceed to obtain explicit expressions for the growth rate of the number of connections at the DPS system for several specific probability distributions. We check through simulations the applicability of our queueing results for modeling TCP connections sharing a bottleneck.     

On the time lag of the effect of network position on service performance in software service networks

We examine whether a time lag exists before the network position of a software service affects its performance. Moreover, we analyze different time lags, using empirical data about software services and their usage for creating composite services. Our results show that software services in central positions (i.e., high betweenness centrality) attract users the most. The highest effect exhibits, if the time lag is 26–32 months. Our findings are relevant, as they can guide developers in marketing their software services and are expected to impact innovation studies regarding the importance of considering time lags and analyzing complementary knowledge.     

Characterizing the measures on the unit circle with exact quadrature formulas in the space of polynomials

In the present paper we characterize the measures on the unit circle for which there exists a quadrature formula with a fixed number of nodes and weights and such that it exactly integrates all the polynomials with complex coefficients. As an application we obtain quadrature rules for polynomial modifications of the Bernstein measures on [−1,1], having a fixed number of nodes and quadrature coefficients and such that they exactly integrate all the polynomials with real coefficients.     

Aggregation in sensor networks with a user-provided quality of service goal

Significant research has been devoted to aggregation in sensor networks with the purpose of optimizing its performance. Existing research has mostly concentrated on maximizing network lifetime within a user-given error bound. In general, the greater the error bound, the longer the lifetime. However, in some situations, it may not be realistic for the user to provide an error bound. Instead, the user may want to provide a quality of service (QoS) goal that has a combined objective of lifetime and error. Indeed, the error tolerable by the user may depend on how long the sensor network can last. This paper presents an aggregation protocol and related algorithms for reaching such a QoS goal. The key idea is to periodically modify a filter threshold for each sensor in a way that is optimal within the user objective, the key technical method being to translate the problem into a mathematical programming formulation with constraints coming from various sources, such as the user, the sensor network, and the data characteristics. Extensive experiments demonstrate the high accuracy, high flexibility and low overhead of this QoS-based optimization approach.     

Simulation for passage times in closed, multiclass networks of queues with unrestricted priorities

Regenerative simulation for passage times in networks of queues with priorities among job classes (and one or more job types) can be based on observation of a fully augmented job stack process which maintains the position of each of the jobs in a linear ‘job stack’, an enumeration of the jobs by service center and job class. In this paper we develop an estimation procedure for passage times through a subnetwork of queues. Observed passage times for all the jobs enter into the construction of point and interval estimates. The confidence intervals obtained using this estimation procedure are shorter than those obtained from simulation using a marked job.     

Point of presence design in Internet protocol networks with performance guarantees

In this paper, we propose a model for the point of presence (POP) design problem in Internet protocol (IP) networks with performance guarantees, where a POP is a node composed of several interconnected co-located backbone routers within a central office. This problem consists of selecting the number of routers and their types, selecting the interface card types, connecting the access and the backbone links to the ports and selecting the link types between the co-located routers. Furthermore, the model considers the routing of the IP traffic. The performance guarantees we refer to are bandwidth guarantees between the routers for the normal state of the POP and also for all failure scenarios of interest to the network planner. A tabu search heuristic to find solutions for real-size instances of the problem is proposed. Finally, we present a systematic set of experiments designed to assess the performance of the proposed heuristic.     

Analysis of file download time in peer-to-peer networks with stochastic and time-varying service capacities

The service capacities of a source peer at different times in a peer-to-peer (P2P) network exhibit temporal correlation. Unfortunately, there is no analytical result which clearly characterizes the expected download time from a source peer with stochastic and time-varying service capacity. The main contribution of this paper is to analyze the expected file download time in P2P networks with stochastic and time-varying service capacities. The service capacity of a source peer is treated as a stochastic process. Analytical results which characterize the expected download time from a source peer with stochastic and time-varying service capacity are derived for the autoregressive model of order 1. Simulation results are presented to validate our analytical results. Numerical data are given to show the impact of the degree of correlation and the strength of noise on the expected file download time. For any chunk allocation method, an analytical result of the expected parallel download time from a source peer with stochastic and time-varying service capacity is derived. It is shown that the algorithm which chooses chunk sizes proportional to the expected service capacities has better performance than the algorithm which chooses equal chunk sizes. It is also shown that multiple source peers do reduce the parallel download time significantly.     

Integrated approach of network reconfiguration with distributed generation and shunt capacitors placement for power loss minimization in radial distribution networks

This article presents the significance of efficient hybrid heuristic search algorithm(HS-PABC) based on Harmony search algorithm (HSA) and particle artificial bee colony algorithm (PABC) in the context of performance enhancement of distribution network through simultaneous network reconfiguration along with optimal allocation and sizing of distributed generators and shunt capacitors. The premature and slow convergence over multi model fitness landscape is the main limitation in standard HSA. In the proposed hybrid algorithm the harmony memory vector of HSA is intelligently enhanced through PABC algorithm during the optimization process to reach the optimal solution within the search space. In hybrid approach, the exploration ability of HSA and the exploitation ability of PABC algorithm are integrated to blend the potency of both algorithms. The box plot and Wilcoxon rank sum tests are used to show the quality of the solution obtained by hybrid HS-PABC with respect to HSA.The computational results prove the integrated approach of the network reconfiguration problem along with optimal placement and sizing of DG units and shunt capacitors as an efficient approach with respect to power loss reduction and voltage profile enhancement. The results obtained on 69 and 118 node network by hybrid HS-PABC method and the standard HSA reveals the effeciency of the proposed approach which guarantees to achieve global optimal solution with less iteration.     

Exploring approaches to improve the performance of autonomous monitoring with imperfect data in location-aware wireless sensor networks

In recent years, information and sensing technologies have been applied to the construction industry to collect and provide rich information to facilitate decision making processes. One of the applications is using location data to support autonomous crane safety monitoring (e.g., collision avoidance and dangerous areas control). Several location-aware wireless technologies such as GPS (Global Positioning System), RFID (Radio-frequency identification), and Ultra-Wide Band sensors, have been proposed to provide location information for autonomous safety monitoring. However, previous studies indicated that imperfections (errors, uncertainty, and inconsistency) exist in the data collected from those sensors and the data imperfections have great impacts on autonomous safety monitoring system performance. This paper explores five computationally light-weight approaches to deal with the data imperfections, aiming to improve the system performance. The authors built a scaled autonomous crane safety monitoring testbed with a mounted localization system to collect location data and developed five representative test cases based on a live construction jobsite. Seven hundred and sixty location readings were collected at thirty-eight test points from the sensors. Those location data was fed into the reasoning mechanisms with five approaches to generate the safety decisions at those thirty-eight test points and evaluate system performance in terms of precision, recall and accuracy. The results indicate that system performance can be improved if at least ten position readings from sensors can be collected at small intervals at any location along the moving path. However, by including additional data such as velocity and acceleration that may be read from devices mounted on workers, localization error may be significantly reduced. These findings represent a path forward to improve localization accuracy by mixing imperfect data from the sensed environment with supplemental input.     

On the performance of adaptive TDMA protocols in WDM passive star networks with fixed transmitters and tunable receivers

An adaptive time division multiple access (TDMA) protocol for WDM passive star networks using fixed transmitters and tunable receivers is presented. The proposed optical adaptive TDMA (OATDMA) protocol is capable of operating efficiently under bursty and correlated traffic. According to the proposed protocol, the stations which are granted permission to transmit at each time slot, are selected by taking into account the network feedback information. In this way, the number of idle slots is minimized and the network performance is significantly improved. Furthermore, although the traffic parameters are unknown and time-variable, the portion of the bandwidth assigned to each station is dynamically adapted to the station’s needs.