Abstract A finite-buffer queueing system with batch Poisson arrivals is considered. A system of integral equations for the distribution function of the number of customers h(t) served before t, conditioned by the initial state of the system, is built. A compact formula for probability generating function of the Laplace transform of distribution of h(t) is […]

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

## Departure Process in Finite-Buffer Queue with Batch Arrivals (Queueing Theory) (Analytical and Stochastic Modeling) Part 2

Numerical Results In this section we present sample numerical results for conditional mean of departures before fixed t i.e. for the expression Enh(t), where the symbol En stands for the mean on condition £(0) = n. In computations we use firstly the following obvious identity: and next the algorithm of approximate numerical Laplace transform inversion […]

## A Two-Class Continuous-Time Queueing Model with Dedicated Servers and Global FCFS Service Discipline (Queueing Theory) (Analytical and Stochastic Modeling) Part 1

Abstract This paper considers a continuous-time queueing model with two types (classes) of customers each having their own dedicated server. The system adopts a "global FCFS" service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. As a consequence of the "global FCFS" rule, customers of one type […]

## A Two-Class Continuous-Time Queueing Model with Dedicated Servers and Global FCFS Service Discipline (Queueing Theory) (Analytical and Stochastic Modeling) Part 2

Comparison of Models and Numerical Examples In this section, we discuss the results obtained in the previous sections, both from a qualitative perspective and by means of some numerical examples. In Figures 3 – 6, we compare both systems studied in section 3 and 4 (i.e., the systems with and without global FCFS) through some […]

## M/G/1 Queue with Exponential Working Vacation and Gated Service (Queueing Theory) (Analytical and Stochastic Modeling) Part 1

Abstract In this paper we consider the analysis of an M/G/1 queue with working vacation. In contrast to the previous literature where the working vacation starts when all customers are served (exhaustive discipline) we consider the case where the vacation period starts when the customers present at the system at beginning of the service period […]

## M/G/1 Queue with Exponential Working Vacation and Gated Service (Queueing Theory) (Analytical and Stochastic Modeling) Part 2

The Stationary Number of Customers at an Arbitrary Epoch In this section we determine the PGF of the stationary number of customers at an arbitrary epoch from the PGFs of the stationary number of customers in the service period and in the vacation period. These PGFs are determined in terms of f (z) and m(z). […]

## The Application of FSP Models in Automatic Optimization of Software Deployment (Software and Computer Systems) (Analytical and Stochastic Modeling) Part 1

Abstract The correct deployment of software objects over the computational resources has a significant impact on the software performance. Achieving the optimal deployment manually is a tedious work as there are many different alternative solutions. In this paper a heuristic algorithm for optimizing the deployment of software objects is proposed which evaluates each deployment in […]

## The Application of FSP Models in Automatic Optimization of Software Deployment (Software and Computer Systems) (Analytical and Stochastic Modeling) Part 2

Implementation We have implemented the deployment algorithm discussed in the previous section using a multi-point hill climbing algorithm. In a multi-point hill-climbing algorithm, a set of arbitrary solutions in the search space are selected as the starting points of the hill-climbing search. By starting from each solution, the algorithm attempts to find a better solution […]

## Model-Based Decision Framework for Autonomous Application Migration (Software and Computer Systems) (Analytical and Stochastic Modeling) Part 1

Abstract A dynamically changing state of the run-time environment impacts the performance of networked applications and furthermore influences the user-perceived quality of the applications. By migrating the application between the user’s devices that give different user experiences, a good overall user experience can be maintained, without loosing the application session. It is non-trivial for a […]

## Model-Based Decision Framework for Autonomous Application Migration (Software and Computer Systems) (Analytical and Stochastic Modeling) Part 2

Generation Approach Impact on Generated Policies To understand the differences between the INS and the MDP generation approaches, we analyse which policies they generate under equal conditions. We use the full parameter spectrum of the environment states, defined by p and q in P (cf. Table 1), since it represents the scope of environment parameters […]