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This paper analyzes a fault-tolerant computer system. The failure/repair behavior of the system is modeled by an irreducible continuous-time Markov chain. Jobs arrive in a Poisson fashion to the system and are serviced according to an FCFS discipline. A failure may cause the loss of the work already done on the job in service, if any; in this case the interrupted job is repeated as soon as the system is ready to deliver service. In addition to the delays due to failures and repairs, jobs suffer delays due to queueing. The authors presents a queueing analysis of fault-tolerant systems and study the steady-state behavior of the number of jobs in the system. As a numerical example, they consider a system with two processors subject to failures and repairs. (Author)

Knowledge on the dynamics of standard epidemic models and their variants over complex networks has been well-established primarily in the stationary regime, with relatively little light shed on their transient behavior. In this paper, we analyze the transient characteristics of the classical susceptible-infected (SI) process with a recovery policy modeled as a state-dependent retrial queueing system in which arriving infected nodes, upon finding all the limited number of recovery units busy, join a virtual buffer and try persistently for service in order to regain susceptibility. In particular, we formulate the stochastic SI epidemic model with added retrial phenomenon as a finite continuous-time Markov chain (CTMC) and derive the Laplace transforms of the underlying transient state probability distributions and corresponding moments for a closed population of size $N$ driven by homogeneous and heterogeneous contacts. Our numerical results reveal the strong influence of infection heterogeneity and retrial frequency on the transient behavior of the model for various performance measures.

Multiuser Multi-Packet Transmission (MPT) from an Access Point (AP) equipped with multiple antennas to multiple single antenna nodes can be achieved by exploiting the spatial dimension of the channel. In this paper we present a queueing model to analytically study such systems from the link-layer perspective, in presence of random packet arrivals and heterogeneous channel conditions. The analysis relies on a blind estimation of the number of different destinations among the packets waiting in the queue, which allows for building a simple, but general model for MPT systems. Simulation results validate the accuracy of the analytical model and provide further insights on the cross-relations between the channel state, the number of antennas, and the number of active users, as well as how they affect the system performance. The simplicity and accuracy of the model makes it suitable for the evaluation of link-layer protocols supporting multiuser MPT in non-saturation conditions, where the queueing dynamics play an important role on the achieved performance.

Bell System Technical Journal, 62: 6. July-August 1983 pp 1433-1453. Asymptotic Analysis of a Queueing Model With Bursty Traffic. (Burman, D.Y.; Smith, D.R.)

We propose a useful approach for investigating the statistical properties of foreign currency exchange rates. Our approach is based on queueing theory, particularly, the so-called renewal-reward theorem. For the first passage processes of the Sony Bank US dollar/Japanese yen (USD/JPY) exchange rate, we evaluate the average waiting time which is defined as the average time that customers have to wait between any instant when they want to observe the rate (e.g. when they log in to their computer systems) and the next rate change. We find that the assumption of exponential distribution for the first-passage process should be rejected and that a Weibull distribution seems more suitable for explaining the stochastic process of the Sony Bank rate. Our approach also enables us to evaluate the expected reward for customers, i.e. one can predict how long customers must wait and how much reward they will obtain by the next price change after they log in to their computer systems. We check the validity of our prediction by comparing it with empirical data analysis.

In studying complex queueing networks, one generally seeks to employ exact analytic solutions to reduce burden on computational resources. Barring the existence of an exact solution, the alternatives include approximation techniques and simulation. Approximation is the more attractive alternative from a time and effort perspective; however, cases exist that are not amiable to this technique. This work increases the flexibility of approximation techniques in obtaining estimates of congestion measures for complex, open queueing networks having several customer classes and class-dependent structures. We accomplish this by providing the procedure to aggregate multiple classes into a single class in order to apply an existing approximation technique. The resulting method is shown to yield good agreement with results obtained by simulation. The immediate application of this work is as a tool to focus a simulation study of multi-class queueing networks. For large networks, reasonable performance estimates can be obtained quickly. Once the basic input parameters are determined, different scenarios may be rapidly evaluated in a fraction of the time needed to modify a typical simulation model. This allows one to check ideas and determine where to invest time and funding when constructing a simulation model to obtain performance estimates on a by-class basis.

Queueing networks with blocking have experienced a dramatic increase in their importance regarding performance evaluation of computer system and communication networks. Parametric Analysis is very interesting for cases in which only one station (e.g., a CPU) in a queueing network model is to be analyzed under various system washload. In order to execute parametric analysis of queueing networks with blocking the problem Computation of the Throughput Values of the Finite Capacity Subsystem is solved.The accuracy of the method has been validated by simulation of several test cases.

Book Source: Digital Library of India Item 2015.229030 dc.contributor.author: D.m. Bhaskar dc.date.accessioned: 2015-07-10T15:52:31Z dc.date.available: 2015-07-10T15:52:31Z dc.date.digitalpublicationdate: 0000-00-00 dc.identifier.barcode: 5990010117919 dc.identifier.origpath: /rawdataupload/upload/0117/921 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/229030 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 74 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Iit Kanpur dc.rights: Out_of_copyright dc.source.library: I I T Kanpur dc.subject.classification: Electrical Engineering dc.title: Implementation Of Gui And Non-blocking Queueing Network Analysis For Qnat

While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with an inhomogeneity at the end. The related model is simple and numerically efficient. It is inspired by models of dynamic queueing networks and takes into account essential features of traffic flows. Instead of treating single vehicles or velocity profiles, it focusses on flows at specific cross sections and average travel times of vehicles.

Book Source: Digital Library of India Item 2015.269742 dc.contributor.author: Anis Ahmad dc.date.accessioned: 2015-07-27T20:35:46Z dc.date.available: 2015-07-27T20:35:46Z dc.identifier.barcode: 05990010890657 dc.identifier.origpath: /data58/upload/0092/374 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/269742 dc.description.scannerno: 20003265 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 229 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Digital Library Of India dc.publisher: Bundelkhand Uni. Jhansi dc.source.library: Bundelkhand Uni. Jhansi dc.subject.classification: Mathematics dc.title: Development And Analysis Of Bulk Queueing Models With Applications dc.type: ptiff dc.type: pdf

Bell System Technical Journal, 62: 10. December 1983 pp 2893-2910. Equivalent Queueing Networks and Their Use in Approximate Equilibrium Analysis. (Kumar, A.)

Bell System Technical Journal, 62: 10. December 1983 pp 2893-2910. Equivalent Queueing Networks and Their Use in Approximate Equilibrium Analysis. (Kumar, A.)

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

The purpose of this research effort was to develop a technique to determine B-1B automatic test equipment station quantities required to support the B-1B avionics components at base level. As part of this effort, both simulation and analytical solutions were developed. A detailed and complex simulation model was developed in the Q-GERT simulation language. In addition, an analytical model was developed based on the theory of open queueing networks and other queueing techniques. However, the analytical model required many crude and simplifying assumptions, and the analytical results were not entirely satisfactory. The Q-GERT simulation model was selected as the best choice for the remainder of the research effort. Two techniques were developed to determine test station quantities based on the model output. The first technique was to buy sufficient test stations to achieve a four day maximum base repair cycle time for the avionics components. The second technique was to conduct a cost-benefit analysis by comparing the costs of additional test stations (and the benefits of shorter repair cycle times) to the benefits of fewer test stations (and the costs of longer repair cycle times). Considerable sensitivity analysis was performed with the simulation model, and the research effort concludes with a range of management options for consideration by the B-1B System Program Office. (Author)

In a recent study [C Arita and D Yanagisawa: J. Stat. Phys. 141, 829 (2010)] the stationary state of a parallel-update TASEP with varying system length, which can be regarded as a queueing process with excluded-volume effect (exclusive queueing process, EQP), was obtained. We analyze the dynamical properties of the number of particles $ < N_t>$ and the position of the last particle (the system length) $ < L_t>$, using an analytical method (generating function technique) as well as a phenomenological description based on domain wall dynamics and Monte Carlo simulations. The system exhibits two phases corresponding to linear convergence or divergence of $ < N_t>$ and $ < L_t>$. These phases can both further be subdivided into high-density and maximal-current subphases. The predictions of the domain wall theory are found to be in very good agreement quantitively with results from Monte Carlo simulations in the convergent phase. On the other hand, in the divergent phase, only the prediction for $ < N_t>$ agrees with simulations.

Multi-hop Cellular Network (MCN) possesses the unique feature of having a fixed infrastructure of Base Station (BS) along with the flexibility of ad-hoc networks. This feature of MCN makes it more suitable for upcoming requirement of cellular network but at the time it increases the overheads required for communication, thus increasing the overall delay. In this paper, a queuing model has been developed to analyze the current cellular network and MCN in terms of Average Waiting Time (AWT) and Channel Utilization. Both the networks consider two types of traffic, namely, voice and data, each prioritizing the voice calls over data traffic. The simulations result is carried out using MATLAB-Simulink. Discrete Event Systems (DES) has been proven to be an effective tool for the study of large and complex systems. The simulation results clearly depict the significance of each network with respect to time.  

Multi-hop Cellular Network (MCN) possesses the unique feature of having a fixed infrastructure of Base Station (BS) along with the flexibility of ad-hoc networks. This feature of MCN makes it more suitable for upcoming requirement of cellular network but at the time it increases the overheads required for communication, thus increasing the overall delay. In this paper, a queuing model has been developed to analyze the current cellular network and MCN in terms of Average Waiting Time (AWT) and Channel Utilization. Both the networks consider two types of traffic, namely, voice and data, each prioritizing the voice calls over data traffic. The simulations result is carried out using MATLAB-Simulink. Discrete Event Systems (DES) has been proven to be an effective tool for the study of large and complex systems. The simulation results clearly depict the significance of each network with respect to time.  

Multi-hop Cellular Network (MCN) possesses the unique feature of having a fixed infrastructure of Base Station (BS) along with the flexibility of ad-hoc networks. This feature of MCN makes it more suitable for upcoming requirement of cellular network but at the time it increases the overheads required for communication, thus increasing the overall delay. In this paper, a queuing model has been developed to analyze the current cellular network and MCN in terms of Average Waiting Time (AWT) and Channel Utilization. Both the networks consider two types of traffic, namely, voice and data, each prioritizing the voice calls over data traffic. The simulations result is carried out using MATLAB-Simulink. Discrete Event Systems (DES) has been proven to be an effective tool for the study of large and complex systems. The simulation results clearly depict the significance of each network with respect to time.  

In this paper, we study a controllable tandem queueing system consisting of two nodes and a controller, in which customers arrive according to a Poisson process and must receive service at both nodes before leaving the system. A decision maker dynamically allocates the number of service resource to each node facility according to the number of customers in each node. In the model, the objective is to minimize the long-run average costs. We cast these problems as Markov decision problems by dynamic programming approach and derive the monotonicity of the optimal allocation policy and the relationship between the two nodes' optimal policy. Furthermore, we get the conditions under which the optimal policy is unique and has the bang-bang control policy property.

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

Cover title

Journal of Research of the National Bureau of Standards

Book Source: Digital Library of India Item 2015.195130 dc.contributor.author: B. Venkataramani dc.date.accessioned: 2015-07-08T05:38:58Z dc.date.available: 2015-07-08T05:38:58Z dc.date.copyrightexpirydate: 0000-00-00 dc.date.digitalpublicationdate: 2029-09-05 dc.identifier: THESIS dc.identifier.barcode: 1990010093860 dc.identifier.origpath: /rawdataupload/upload/0093/860 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/195130 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 345 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: I.i.t Kan dc.rights: Out_of_copyright dc.source.library: I.i.t Kanpur dc.subject.classification: Science dc.title: Queueing Analysis Of A Non-preemptive Mmpp-d-1-k Priority Sys dc.rights.holder: Not Available

The Rajasthan Government has passed a “Right to Health Bill 2023” on March,21 and became the first state to enact a Right to Health Act. The bill gives every resident of the state the right to avail free Out Patient Department (OPD) services and in Patient Department (IPD) services at all public health facilities. The bill sparked massive protests from the medical community. In this article, we analysis the requirement of this bill and problems in implementation of RTH. Does this bill play a significant role to improve health care system at local level? We also discuss the practical situation of hospitals system capacity for these types of revolution. Here we use Queueing theory techniques for manpower planning in hospitals to improve efficiency of healthcare system. This is a theoretical article and provide decision support system for Policymakers and Public administration.

The Rajasthan Government has passed a “Right to Health Bill 2023” on March,21 and became the first state to enact a Right to Health Act. The bill gives every resident of the state the right to avail free Out Patient Department (OPD) services and in Patient Department (IPD) services at all public health facilities. The bill sparked massive protests from the medical community. In this article, we analysis the requirement of this bill and problems in implementation of RTH. Does this bill play a significant role to improve health care system at local level? We also discuss the practical situation of hospitals system capacity for these types of revolution. Here we use Queueing theory techniques for manpower planning in hospitals to improve efficiency of healthcare system. This is a theoretical article and provide decision support system for Policymakers and Public administration.

Book Source: Digital Library of India Item 2015.193354 dc.contributor.author: Umesh.m.n dc.date.accessioned: 2015-07-08T02:34:38Z dc.date.available: 2015-07-08T02:34:38Z dc.date.digitalpublicationdate: 2005-08-27 dc.identifier.barcode: 1990010091694 dc.identifier.origpath: /rawdataupload/upload/0091/694 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/193354 dc.description.scannerno: 14 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 62 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Mechanical Engineering In General. Nuclear Technology. Electrical Engineering. Machinery dc.title: A Window Based Package For Queueing Network Analysis

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

A CSMA/CD local area network consists of single server (the channel) and multiple interacting queues of message packets. The message queueing process in a buffered, P-persistent CSMA/CD system is modeled as a multidimensional semi-markov chain. An effective approximation method to compute the mean packet delay in equilibrium is developed, based on the joint probability generating function of the queue length vector at embedded Markov epochs. We also develop a simulation model to validate approximation results. To the best of our knowledge, this work is the first in the literature that enables optimization of the control parameter P for the CSMA/CD system with more than two users. (Author)

The bike sharing systems are fast increasing as a public transport mode in urban short trips, and have been developed in many major cities around the world. A major challenge in the study of bike sharing systems is that large-scale and complex queueing networks have to be applied through multi-dimensional Markov processes, while their discussion always suffers a common difficulty: State space explosion. For this reason, this paper provides a mean-field computational method to study such a large-scale bike sharing steps: Firstly, a multi-dimensional Markov process is set up for expressing the states of the bike sharing system, and the empirical process of the multi-dimensional Markov process is given to partly overcome the difficulty of state space explosion. Based on this, the mean-field equations are derived by means of a virtual time-inhomogeneous M(t)/M(t)/1/K queue whose arrival and service rates are determined by the mean-field computation. Secondly, the martingale limit is employed to investigate the limiting behavior of the empirical process, the fixed point is proved to be unique so that it can be computed by means of a nonlinear birth-death process, the asymptotic independence of this system is discussed simply, and specifically, these lead to numerical computation of the steady-state probability of the problematic (empty or full) stations. Finally, some numerical examples are given for valuable observation on how the steady-state probability of the problematic stations depends on some crucial parameters of the bike sharing system.

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

This is a dump of the companion floppy to "Practical Queueing Analysis" by Mike Tanner.

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

A logical classification of multiprocessor structures from the point of view of control applications is presented. A computation of the response time distribution for a canonical model of a real time multiprocessor is presented. The multiprocessor is approximated by a blocking model. Two separate models are derived: one created from the system's point of view, and the other from the point of view of an incoming task.

Includes bibliographies and index

Synchronous time division multiplexing is analyzed. Packets of information arrive at the system as a compound Poisson process, and are transmitted only during individual periodic intervals. Packet arrivals are blocked (lost) if the system has a finite capacity and is congested. Using the theory of semiregenerative processes, the distribution of the number of packets in the system (system size) is found. This nonstationary distribution is used to determine the complete system behavior, including the delay distributions, the blocking probability, and the density of the system size at arrival instants. Numerical examples illustrate applications of the results given.

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

In this article statistical bounds for certain output characteristics of the $M/GI/1/n$ and $GI/M/1/n$ loss queueing systems are derived on the basis of large samples of an input characteristic of these systems, such as service time in the $M/GI/1/n$ queueing system or interarrival time in the $GI/M/1/n$ queueing system. The analysis of this article is based on application of Kolmogorov's statistics for empirical probability distribution functions.

In this article statistical bounds for certain output characteristics of the $M/GI/1/n$ and $GI/M/1/n$ loss queueing systems are derived on the basis of large samples of an input characteristic of these systems, such as service time in the $M/GI/1/n$ queueing system or interarrival time in the $GI/M/1/n$ queueing system. The analysis of this article is based on application of Kolmogorov's statistics for empirical probability distribution functions.

We study the performance of random linear network coding for time division duplexing channels with Poisson arrivals. We model the system as a bulk-service queue with variable bulk size. A full characterization for random linear network coding is provided for time division duplexing channels [1] by means of the moment generating function. We present numerical results for the mean number of packets in the queue and consider the effect of the range of allowable bulk sizes. We show that there exists an optimal choice of this range that minimizes the mean number of data packets in the queue.

In this paper, information theoretic inference methodology for system modeling is applied to estimate the probability distribution for the number of customers in a general, single server queueing system with infinite capacity utilized by an infinite customer population. Limited to knowledge of only the mean number of customers and system equilibrium, entropy maximization is used to obtain an approximation for the number of customers in the G{G}1 queue. This maximum entropy approximation is exact for the case of G=M i.e., the M{M}1 queue. Subject to both independent and dependent information, an estimate for the joint customer distribution for queueing systems in tandem is presented. Based on the simulation of two queues in tandem, numerical comparisons of the joint maximum entropy distribution is given. These results serve to establish the validity of the inference technique and as an introduction to information theoretic approximation to queueing networks.

In this paper, information theoretic inference methodology for system modeling is applied to estimate the probability distribution for the number of customers in a general, single server queueing system with infinite capacity utilized by an infinite customer population. Limited to knowledge of only the mean number of customers and system equilibrium, entropy maximization is used to obtain an approximation for the number of customers in the G{G}1 queue. This maximum entropy approximation is exact for the case of G=M i.e., the M{M}1 queue. Subject to both independent and dependent information, an estimate for the joint customer distribution for queueing systems in tandem is presented. Based on the simulation of two queues in tandem, numerical comparisons of the joint maximum entropy distribution is given. These results serve to establish the validity of the inference technique and as an introduction to information theoretic approximation to queueing networks.

Understanding the detailed queueing behavior of a networking session is critical in enabling low-latency services over the Internet. Especially when the packet arrival and service rates at the queue of a link vary over time and moreover when the session is short-lived, analyzing the corresponding queue behavior as a function of time, which involves a transient analysis, becomes extremely challenging. In this paper, we propose and develop a new analytical framework that anatomizes the transient queue behavior under time-varying arrival and service rates even under unstable conditions. Our framework is capable of answering key questions in designing low-latency services such as the time-dependent probability distribution of the queue length; the instantaneous or time-averaged violation probability that the queue length exceeds a certain threshold; and the fraction of time during an interval $[0, t]$ at which the queue length exceeds a certain threshold. We validate our framework by comparing its prediction results over time with the statistical simulation results and confirm that our analysis is accurate enough. Our extensive demonstrations on the efficacy of the analytical framework in designing low-latency services reveal that its prediction ability for the transient queue behavior in diverse time-varying packet arrival and service patterns can be of a high practical value.

Queueing network models have achieved a prominent place in the modelling of computer system performance. Recent formulations of operational methods by Buzen and others have greatly facilitated their practical use. On the other hand, Kolence's software physics has addressed the problem of appropriate metrics for both performance and capacity of processors and systems and for the workloads with which they interact. This paper integrates the methods of operational queueing network analysis into an extension of software physics. A significant feature of this approach is that parameters of the equipment and of the workload are not confounded in the analysis but are kept distinct, finally combining in the model computations proper. The objectives, principles and assumptions are stated and the basic quantities are defined. The fundamental operational laws and certain of the algorithms are derived and illustrated with examples. (Author)

This dissertation contians studies in two related areas: Discrete Event Systems Theory and Queueing Network Theory. In the first line of study, deterministic discrete event systems are modeled by formal automata- like structures, and a hierarchy of morphic relations among them is developed. A canonical representation of stochastic discrete event systems in coordinate probability space is proposed, and a hierarchy of morphic relations among them is constructed by means of measure preserving transformations. In the second line of study, several operating characteristics of the class of Jackson queueing networks are investiaged. Included are: line sizes (network state), total service awarded to customers, and traffic processes on the arcs. Special emphasis is placed on rigorous derivations of results from solid mathematical and statistical foundations. In the process, a number of theoretical gaps in the extant theory of state equilibrium are closed, and Burke's Theorem is extended from M/M/1 queues to Jackson networks with single server nodes.

This dissertation contians studies in two related areas: Discrete Event Systems Theory and Queueing Network Theory. In the first line of study, deterministic discrete event systems are modeled by formal automata- like structures, and a hierarchy of morphic relations among them is developed. A canonical representation of stochastic discrete event systems in coordinate probability space is proposed, and a hierarchy of morphic relations among them is constructed by means of measure preserving transformations. In the second line of study, several operating characteristics of the class of Jackson queueing networks are investiaged. Included are: line sizes (network state), total service awarded to customers, and traffic processes on the arcs. Special emphasis is placed on rigorous derivations of results from solid mathematical and statistical foundations. In the process, a number of theoretical gaps in the extant theory of state equilibrium are closed, and Burke's Theorem is extended from M/M/1 queues to Jackson networks with single server nodes.