Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

Performance analysis of realistic true proportional navigation against maneuvering targets using Lyapunov-like approach

At most traditional signalized intersections, three types of phasing can be provided to left turns: protected only phasing, permitted only phasing, and a combination of protected and permitted phasing (protected/permitted phasing). While numerous guidelines for the selection of left-turn phasing have been developed, there is no widely recognized guideline or criterion for the use of left-turn phasing under specific traffic conditions especially for a single left-turn lane. Focusing on the inherent mechanism of the dynamic nature and uncertainty of left-turn queues under different left-turn phasing, this paper develops a left-turn queueing model with uncertain second vacation to analytically evaluate the performance of left turns for different left-turn phasing, which considers various factors including the type of left-turn phasing, signal timing, left-turn volume, opposing through volume, type of left-turn lane, number of opposing through lanes, and number of sneakers, etc. For different left-turn phasing, the left-turn queues formation and dissipation with different characteristics of vacations (i.e., server absences during the red time and uncertain blocked time caused by the opposing through flow during the permitted green time) are formulated, and the queue length distributions of left turns along with the time within one cycle and at an arbitrary time are derived. Furthermore, three sets of left-turn performance measures are obtained: primary queueing measures, fuel-consumption (or emissions) related measures, and safety related measure. On the basis of these performance measures, an analytical evaluation framework for left-turn queues is established, which can provide a more accurate and detailed basis for evaluating and improving the use of left-turn phasing. Model validation indicates that the proposed model can be an effective tool to evaluate the use of left-turn phasing under different traffic conditions. In addition, numerical experiments are also performed to theoretically identify the factors that could affect the performance of left turns and thus help to determine the left-turn phasing selection under different conditions.

Analytical evaluation of the use of left-turn phasing for single left-turn lane only

True proportional navigation (TPN) guidance law is widely used for exoatmospheric interception, for its robustness and ease of implementation. The performance of TPN against nonmaneuvering target or the maneuvering target with a specific acceleration had been analyzed before. However, the obtained results are not suitable for the realistic exoatmospheric interception scenario, since the target may maneuver along an arbitrary direction with an arbitrary but upper-bounded acceleration in the three-dimensional (3D) space, which is the so-called “true-arbitrarily maneuvering target” in this paper. With the help of the line-of-sight (LOS) rotation coordinate system, the performance of 3D TPN against the true-arbitrarily maneuvering target is thoroughly analyzed using the Lyapunov-like approach. The upper-bound of the 3D LOS rate is obtained, and so is that of the commanded acceleration of 3D TPN. After that, the capture region of 3D TPN is presented on the initial relative velocity plane. The nonlinear 3D relative kinematics between the interceptor and the target is taken into full account. Finally, the new theoretical findings are demonstrated by numerical simulations.

Performance of 3D TPN against true-arbitrarily maneuvering target for exoatmospheric interception

Accounting for the missile autopilot as second-order dynamics, a dimension reduction observer-based guidance law is designed using the dynamic surface control method. Certain first-order low-pass f...

A dimension reduction observer-based guidance law accounting for dynamics of missile autopilot

Mixed vehicular traffic comprising small cars and two-wheeled vehicles (called motorcycles in this paper) arrive at a lane of a signalized road intersection. The traffic does not follow lane-discipline, in that the arriving vehicles do not necessarily queue up one behind the other. The motorcycles are small enough to stand side-by-side with cars or other motorcycles, so as to fill up the width of the lane. With such queue joining behavior, the waiting vehicles form batches, comprising motorcycles, and at most one car. During the green signal period the vehicles in the head-of-the-line batch exit the intersection together. In this paper, assuming a Poisson point process model for vehicle arrivals, we have provided an approximate analysis of such a queueing system. Our approach is to use an assembly queue model for the batching process. The batches generated by the assembly queue enter an interrupted M/SemiMarkov/1 (or M/SM/1) queue. By analyzing the assembly queue we characterize the batch input process for the interrupted M/SM/1 queue. We then develop an extension of the Webster mean delay formula for obtaining the approximate mean delay in the interrupted M/SM/1 queue. Numerical results from the analysis are compared with simulation results. The analysis is shown to be accurate in predicting the increase in the system capacity due to the batching behavior.

Approximate Mean Delay Analysis for a Signalized Intersection With Indisciplined Traffic

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

In many practical systems concerning linear system identification with adaptive filters, the performance of the system is intrinsically limited by the problem of missing data, which might arise either because the input or the output data is missing at random time instants or subsets of input or output data are missing. In this paper the problem of linear system identification is studied with only input data missing at random time instants while output data is obtained correctly at all time instants. To model the input data missing process, the available input data sequence is modeled as the product of the actual (unknown) input data sequence with an i.i.d. sequence of Bernoulli random variables with known mean. A new data sequence, called the imputed data sequence is created from the available data sequence where, at any time instant, the imputed data is either the available data at that instant, if it is nonzero, or is set to a constant factor times the imputed data at the previous time instance. This imputed sequence is then used to propose an LMS-type algorithm called Imputation based missing data LMS (ImdLMS). Performance analysis of the algorithm is carried out where the extreme complications and possible intractability vis-a-vis an exact mean square performance analysis is avoided by finding an upper bound of the mean square deviation of the algorithm. Simulation results demonstrate the efficacy of the proposed ImdLMS algorithm, especially when the actual (unknown) input data sequence is correlated.

ImdLMS: An Imputation Based LMS Algorithm for Linear System Identification With Missing Input Data

Recovery of an unknown sparse signal from a few of its projections is the key objective of compressed sensing. Often one comes across signals that are not ordinarily sparse but are sparse blockwise. Existing block sparse recovery algorithms like BOMP make the assumption of uniform block size and known block boundaries, which are, however, not very practical in many applications. This paper addresses this problem and proposes a two step procedure, where the first stage is a coarse block location identification stage while the second stage carries out finer localization of a non-zero cluster within the window selected in the first stage. A detailed convergence analysis of the proposed algorithm is carried out by first defining the so-called pseudoblock-interleaved block RIP of the given generalized block sparse signal and then imposing upper bounds on the corresponding RIC. We also extend the analysis for complex vector as well as matrix entries where it turns out that the extension is non-trivial and requires special care. Furthermore, assuming real Gaussian sensing matrix entries, we find a lower bound on the probability that the derived recovery bounds are satisfied. The lower bound suggests that there are sets of parameters such that the derived bound is satisfied with high probability. Simulation results confirm significantly improved performance of the proposed algorithm as compared to BOMP.

Samrat Mukhopadhyay

Papers

Approximate Mean Delay Analysis for a Signalized Intersection With Indisciplined Traffic

Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

ImdLMS: An Imputation Based LMS Algorithm for Linear System Identification With Missing Input Data

A Two Stage Generalized Block Orthogonal Matching Pursuit (TSGBOMP) Algorithm

Stochastic gradient descent for linear systems with sequential matrix entry accumulation