Preface to the Second Edition. First 1. Introduction. 1.1 Motivation. 1.2 Methodological Background. 1.3 Basics of Probability and Statistics. 2. Markov Chains. 2.1 Processes. 2.2 Performance Measures. 2.3 Generation Methods. 3. Steady-State Solutions 3.1 Solution for a Birth Death Process. 3.2 Matrix-Geometric Method: Quasi-Birth-Death 3.3 Hessenberg Matrix: Non-Markovian Queues. 3.4 Numerical Solution: Direct 3.5 Iterative 3.6 Comparison 4. Aggregation/Disaggregation 4.1 Courtois'...

General characterizations of geometric convergence for Markov chains in discrete time on a general state space have been developed recently considerable detail. Here we develop similar theory $\varphi$-irreducible continuous processes and consider the following types criteria convergence: 1. existence exponentially bounded hitting times one then all suitably "small" sets; 2. "Foster-Lyapunov" or "drift" conditions any skeleton resolvent chains; 3. drift extended generator $\tilde\mathscr{A}$...

In this paper we study open generalized Jackson networks with general arrival streams and service time distributions. Assuming that the rate does not exceed network capacity times possess conditionally bounded second moments, deduce stability of by bounding expected waiting for a customer entering network. For Markovian obtain convergence total work in system, as well mean queue size delay, to unique finite steady state value.

Platelet products are both expensive and have very short shelf lives. As usage rates for platelets highly variable, the effective management of platelet demand supply is important yet challenging. The primary goal this paper to present an efficient forecasting model at Canadian Blood Services (CBS). To accomplish goal, five different methods, ARIMA (Auto Regressive Integrated Moving Average), Prophet, lasso regression (least absolute shrinkage selection operator), random forest, LSTM (Long...

For a system of finite queues, we study how servers should be assigned dynamically to stations in order obtain optimal (or near-optimal) long-run average throughput. We assume that travel times between different service facilities are negligible, each server can work on only one job at time, and several together job. show when the rates depend either or station (and not both), then all nonidling assignment policies optimal. Moreover, for Markovian with two tandem servers, policy assigns...

This paper is concerned with the design of dynamic server assignment policies that maximize capacity queueing networks flexible servers. Flexibility here means each may be capable performing service at several different classes in network. We assume interarrival times and are independent identically distributed, routing probabilistic. also allow for switching times, which we to distributed. deduce value a tight upper bound on achievable by equating network model limiting deterministic fluid...

We consider a single-server queue with renewal arrivals and i.i.d. service times in which the server uses shortest remaining processing time policy. To describe evolution of this queue, we use measure-valued process that keeps track residual all buffered jobs. propose fluid model (or formal law large numbers approximation) for system and, under mild assumptions, prove existence uniqueness solutions. Furthermore, scaling limit theorem justifies as first-order approximation stochastic model....

The scalability of Cloud infrastructures has significantly increased their applicability. Hadoop, which works based on a MapReduce model, provides for efficient processing Big Data. This solution is being used widely by most providers. Hadoop schedulers are critical elements providing desired performance levels. A scheduler assigns tasks to resources. There considerable challenge schedule the growing number and resources in scalable manner. Moreover, potential heterogeneous nature deployed...

The demand and supply of blood are highly variable over time. Blood inventory management that relies heavily on experience-based decisions may not be adaptive to real demand, leading high operational costs, wastage, shortages.We combined statistical modeling, machine learning, optimization methods develop a data-driven forecasting strategy for red cells (RBCs). We then used the inform daily orders. A secondary semi-weekly (twice per week) ordering was developed handle last-mile split...

A fundamental aspect of designing systems with dedicated servers is identifying and improving the system bottlenecks. We extend concept a bottleneck to networks heterogeneous, flexible servers. In contrast network servers, bottlenecks are not priori obvious, but can be determined by solving number linear programming problems. Unlike server case, we find that may span several nodes in network. then identify some characteristics desirable flexibility structures. particular, chosen structure...

With the current high levels of energy consumption data centers, reducing power by even a small percentage is beneficial. We propose framework for thermal-aware workload distribution in center to reduce cooling consumption. The includes linearization general optimization problem and proposing heuristic approximate solution resulting Mixed Integer Linear Programming (MILP) problems. first define nonlinear including several parameters, heat recirculation effects, constraints on server...

Presents an algorithm that allows the computer automation of analysis stability re-entrant lines. Through various examples, it is suggested this method may completely characterise region for types networks considered. For class non-idling and buffer priority policies, piecewise linear functions low complexity are constructed. To construct such other policies as FIFO appears to be more difficult in general, due complex state representation models.< <ETX...

In this paper, we present a technique to model and analyse cryptographic protocols using coloured petri nets. A of the protocol is constructed in top-down manner: first modeled without an intruder, then generic intruder added. The illustrated on TMN protocol, with several mechanisms introduced reduce size occurrence graph. smaller graph facilitates deducing whether particular security goals are met.