A Markov Chain Model Checker

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [17,6] and the continuous time setting [4,8]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen Twente Markov Chain Checker $(E \vdash MC^2$), where properties are expressed in appropriate extensions of CTL. We illustrate the general bene ts of this approach and discuss the structure of the tool. Furthermore we report on first successful applications of the tool to non-trivial examples, highlighting lessons learned during development and application of $(E \vdash MC^2$)

Representative queueing network models of computer systems in terms of time delay probability distributions

Imperial Users onl

Laws of Little in an open queueing network

The object of this research in the queueing theory is theorems about the functional strong laws of large numbers (FSLLN) under the conditions of heavy traffic in an open queueing network (OQN). The FSLLN is known as a fluid limit or fluid approximation. In this paper, FSLLN are proved for the values of important probabilistic characteristics of the OQN investigated as well as the virtual waiting time of a customer and the queue length of customers. As applications of the proved theorems laws of Little in OQN are presented

A Survey on Delay-Aware Resource Control for Wireless Systems --- Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning

In this tutorial paper, a comprehensive survey is given on several major systematic approaches in dealing with delay-aware control problems, namely the equivalent rate constraint approach, the Lyapunov stability drift approach and the approximate Markov Decision Process (MDP) approach using stochastic learning. These approaches essentially embrace most of the existing literature regarding delay-aware resource control in wireless systems. They have their relative pros and cons in terms of performance, complexity and implementation issues. For each of the approaches, the problem setup, the general solution and the design methodology are discussed. Applications of these approaches to delay-aware resource allocation are illustrated with examples in single-hop wireless networks. Furthermore, recent results regarding delay-aware multi-hop routing designs in general multi-hop networks are elaborated. Finally, the delay performance of the various approaches are compared through simulations using an example of the uplink OFDMA systems.Comment: 58 pages, 8 figures; IEEE Transactions on Information Theory, 201

A Stochastic Model for Joint Reception, Staging, Onward Movement, and Integration (JRSOI)

A stochastic model for the performance evaluation of a key phase in the deployment process, namely Joint Reception, Staging, Onward Movement, and Integration (JRSOI) is presented. The process is modeled as an open, multi-class tandem queueing network wherein personnel and various classes of cargo are modeled as the flow entities and the stages of the process constitute individual queueing stations. Single and multiple-class models at both low and high resolutions are presented. No analytical stochastic model of this process currently exists in the literature or in practice. The model provides a quick look at key aggregate performance measures such as system throughput and closure, and can be used to expediently identify problems occurring during JRSOI and the impact they have on the process. This information can substantially aid decision makers in regulating process flow. The queueing network model developed here can easily be expanded and adapted to any potential area of conflict. Numerical comparisons with Monte-Carlo simulation demonstrate that the model provides a viable, novel approach to the problem

The evaluation of computer performance by means of state-dependent queueing network models

Imperial Users onl

Proportional switching in FIFO networks

We consider a family of discrete time multihop switched queueing networks where each packet movesalong a xed route. In this setting, BackPressure is the canonical choice of scheduling policy; this policy hasthe virtues of possessing a maximal stability region and not requiring explicit knowledge of tra c arrival rates.BackPressure has certain structural weaknesses because implementation requires information about each route,and queueing delays can grow super-linearly with route length. For large networks, where packets over manyroutes are processed by a queue, or where packets over a route are processed by many queues, these limitationscan be prohibitive.In this article, we introduce a scheduling policy for FIFO networks, the Proportional Scheduler, which isbased on the proportional fairness criterion. We show that, like BackPressure, the Proportional Scheduler hasa maximal stability region and does not require explicit knowledge of tra c arrival rates. The ProportionalScheduler has the advantage that information about the network's route structure is not required for scheduling,which substantially improves the policy's performance for large networks. For instance, packets can be routedwith only next-hop information and new nodes can be added to the network with only knowledge of thescheduling constraintsThe research of the rst author was partially supported by NSF grants DMS-1105668 and DMS-1203201. The research of the second author was partially supported by the Spanish Ministry of Economy and Competitiveness Grants MTM2013-42104-P via FEDER funds; he thanks the ICMAT (Madrid, Spain) Research Institute that kindly hosted him while developing this project

General queueing network models for computer system performance analysis. A maximum entropy method of analysis and aggregation of general queueing network models with application to computer systems.

In this study the maximum entropy formalism [JAYN 57] is suggested as an alternative theory for general queueing systems of computer performance analysis. The motivation is to overcome some of the problems arising in this field and to extend the scope of the results derived in the context of Markovian queueing theory. For the M/G/l model a unique maximum entropy solution., satisfying locALl balance is derived independent of any assumptions about the service time distribution. However, it is shown that this solution is identical to the steady state solution of the underlying Marko-v process when the service time distribution is of the generalised exponential (CE) type. (The GE-type distribution is a mixture of an exponential term and a unit impulse function at the origin). For the G/M/1 the maximum entropy solution is identical in form to that of the underlying Markov process, but a GE-type distribution still produces the maximum overall similar distributions. For the GIG11 model there are three main achievements: first, the spectral methods are extended to give exaft formulae for the average number of customers in the system for any G/G/l with rational Laplace transform. Previously, these results are obtainable only through simulation and approximation methods. (ii) secondly, a maximum entropy model is developed and used to obtain unique solutions for some types of the G/G/l. It is also discussed how these solutions can be related to the corresponding stochastic processes. (iii) the importance of the G/GE/l and the GE/GE/l for the analysis of general networks is discussed and some flow processes for these systems are characterised. For general queueing networks it is shown that the maximum entropy solution is a product of the maximum entropy solutions of the individual nodes. Accordingly, existing computational algorithms are extended to cover general networks with FCFS disciplines. Some implementations are suggested and a flow algorithm is derived. Finally, these results are iised to improve existing aggregation methods. In addition, the study includes a number of examples, comparisons, surveys, useful comments and conclusions