Abstract Garbage collection represents an important feature of many modern systems that allows programmers to avoid explicit memory management and related common errors. However, its usage introduces problems in software performance engineering, because on the one hand the system exhibits better performances when there is low memory occupancy and on the other hand the garbage […]

# Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2011)

## Optimisation of Virtual Machine Garbage Collection Policies (Software and Computer Systems) (Analytical and Stochastic Modeling) Part 2

Heuristic for Minimal Average Response Time In this section we discuss an application of the proposed model to define a heuristic for determining the optimum activation rate in a system with garbage collection. In practice, we aim to determine, in flight, the optimum garbage collector activation rate ai. Assume that given a system with B […]

## Performance Evaluation of a Single Node with General Arrivals and Service (Queueing Theory) (Analytical and Stochastic Modeling)

Abstract Queueing delays experienced by packets buffered at a node are among the most difficult to predict when considering the performance of a flow in a network. The arrivals of packets at a node tend to be highly variable so that a finite-buffer single-server queue with general arrivals and service emerges as a natural model […]

## Tandem Queueing System with Different Types of Customers (Queueing Theory) (Analytical and Stochastic Modeling) Part 1

Abstract A dual tandem consisting of multi-server queueing systems without buffers is considered. Customers of two types arrive to Station 1 in the MMAP (Marked Markovian Arrival Process). The first type customers aim to be served at Station 1 only while the second type customers should be served at both stations. The stationary distribution of […]

## Tandem Queueing System with Different Types of Customers (Queueing Theory) (Analytical and Stochastic Modeling) Part 2

Numerical Results In the numerical experiment, we solve the problem of optimal choice of the number N of servers at Station 1 and the number R of servers at Station 2. We consider the following cost criterion (an average gain per unit time under the steady-state operation of the system) of the system operation: where […]

## Fast Evaluation of Appointment Schedules for Outpatients in Health Care (Queueing Theory) (Analytical and Stochastic Modeling) Part 1

Abstract We consider the problem of evaluating an appointment schedule for outpatients in a hospital. Given a fixed-length session during which a physician sees K patients, each patient has to be given an appointment time during this session in advance. When a patient arrives on its appointment, the consultations of the previous patients are either […]

## Fast Evaluation of Appointment Schedules for Outpatients in Health Care (Queueing Theory) (Analytical and Stochastic Modeling) Part 2

Assisted Sequential Scheduling Cost Function The ‘quality’ of a schedule depends on the importance attributed to certain aspects of its performance. For example, it is a usual goal to keep the expected patient waiting times as low as possible, but not at the expense of an excessive physician idle time or session overtime. In most […]

## Technique of Statistical Validation of Rival Models for Fatigue Crack Growth Process and Its Identification (Statistics Inference) (Analytical and Stochastic Modeling) Part 1

Abstract The development of suitable models of stochastic crack growth process is important for the reliability analysis of fatigued structures as well as the scheduling of inspection and repair/replacement maintenance. Based on modifications of the solution of the deterministic differential equation for the crack growth rate, where a stochastic nature of this rate is expressed […]

## Technique of Statistical Validation of Rival Models for Fatigue Crack Growth Process and Its Identification (Statistics Inference) (Analytical and Stochastic Modeling) Part 2

Test for the Operational Validity The test of H0(k) versus H1(k), based on vn(k), is given by where h(k)>0 is a threshold of the test which is determined for a prescribed level of significance a(k) as of the F-distribution with 1 and n-1 degrees of freedom. When the parameteris unknown, it is well known that […]

## Suitability of the M/G/∞ Process for Modeling Scalable H.264 Video Traffic (Statistics Inference) (Analytical and Stochastic Modeling)

Abstract Video represents a larger and larger portion of the traffic in Internet. H.264/AVC and its scalability extension have recently become some of the most widely accepted video coding standards. Consequently, adequate models for this traffic are very important for the performance evaluation of networks architectures and protocols. Particularly, the efficient and on-line generation of […]