Muhammad A. Qureshi

The UltraSAN modeling environment

Abstract Model-based evaluation of computer systems and networks is an increasingly important activity. For modeling to be used effectively, software environments are needed that ease model specification, construction, and solution. Easy to use, graphical methods for model specification that support solution of families of models with differing parameter values are also needed. Since no model solution technique is ideal for all situations, multiple analysis and simulation-based solution techniques should be supported. This paper describes UltraSAN , one such software environment. The design of UltraSAN reflects its two main purposes: to facilitate the evaluation of realistic computer systems and networks, and to provide a test-bed for investigating new modeling techniques. In UltraSAN , models are specified using stochastic activity networks, a stochastic variant of Petri nets, using a graphical X-Window based interface that supports large-scale model specification, construction, and solution. Models may be parameterized to reduce the effort required to solve families of models, and a variety of analysis and simulation-based solution techniques are supported. The package has a modular organization that makes it easy to add new construction and solution techniques as they become available. In addition to describing the features, capabilities, and organization of UltraSAN , the paper illustrates the use of the package in the solution for the unreliability of a fault-tolerant multiprocessor using two solution techniques.

Reward model solution methods with impulse and rate rewards: an algorithm and numerical results

Abstract Reward models have become an important method for specifying performability models for many types of systems. Many methods have been proposed for solving reward models, but no method has proven itself to be applicable over all system classes and sizes. Furthermore, specification of reward models has usually been done at the state level, which can be extremely cumbersome for realistic models. We describe a method to specify reward models as stochastic activity networks (SANs) with impulse and rate rewards, and a method by which to solve these models via uniformization. The method is an extension of one proposed by de Souza e Silva and Gail in which impulse and rate rewards are specified at the SAN level, and solved in a single model. Furthermore, we propose a new technique for discarding paths in the uniformized process whose contribution to the reward variable is minimal, which greatly reduces the time and space required for a solution. A bound is calculated on the error introduced by this discarding, and its effectiveness is illustrated through the study of the performability and availability of a degradable multi-processor system.

A new methodology for calculating distributions of reward accumulated during a finite interval

Markov reward models are an important formalism by which to obtain dependability and performability measures of computer systems and networks. In this context, it is particularly important to determine the probability distribution function of the reward accumulated during a finite interval. The interval may correspond to the mission period in a mission-critical system, the time between scheduled maintenances, or a warranty period. In such models, changes in state correspond to changes in system structure (due to faults and repairs), and the reward structure depends on the measure of interest. For example, the reward rates may represent a productivity rate while in that state, if performability is considered, or the binary values zero and one, if interval availability is of interest. We present a new methodology to calculate the distribution of reward accumulated over a finite interval. In particular, we derive recursive expressions for the distribution of reward accumulated given that a particular sequence of state changes occurs during the interval, and we explore paths one at a time. The expressions for conditional accumulated reward are new and are numerically stable. In addition, by exploring paths individually, we avoid the memory growth problems experienced when applying previous approaches to large models. The utility of the methodology is illustrated via application to a realistic fault-tolerant multiprocessor model with over half a million states.

The effect of workload on the performance and availability of voting algorithms

Voting algorithms are a popular way to provide data consistency in replicated data systems. By maintaining multiple copies of data on distinct servers, they can increase the datas availability, as perceived by a user. Many models have been made to study the degree to which replication increases the availability of data, and some have been made to study the cost incurred in maintaining consistency. However, little work has been done to evaluate the time it takes to serve a request, accounting for server and network failures, or to determine the effect of workload on these measures. The effect of workload can be significant, since failures of system components are not important unless they are needed to deliver a service, and requests can force updates on data that would otherwise be outdated. In this paper, we use stochastic activity networks (SANs), a variant of stochastic Petri nets, to construct two variant models of a replicated file system, one using a static voting algorithm while the other using a dynamic voting algorithm to maintain data consistency. A Markov process representation is automatically constructed from each SAN model and is solved numerically. Specifically, we determine the availability and mean time to respond to write requests as a function of the number of replicated copies and workload offered to the system. The results illustrate that it is indeed possible to determine such measures analytically and that workload, as well as the number of copies, is an important determinant of availability and response time.

Expected Impulsive Rewards in Markov Regenerative Stochastic Petri Nets

Reward structures provide a versatile tool for the definition of performance and dependability measures in stochastic Petri nets. In this paper we derive formulas for the computation of expected reward measures in Markov regenerative stochastic Petri nets, which allow for transitions with non-exponentially distributed firing times. The reward measures may be composed of rate rewards which are obtained in certain markings and of impulse rewards which are obtained when transitions fire. The main result of the paper is the derivation of formulas for the expected impulse reward of transitions with non-exponentially distributed firing times. The analysis is based on the method of supplementary variables. Numerical examples are given for an M/D/1/K queueing system with service breakdowns.

Performability modeling with UltraSAN

The utility of stochastic activity networks (SANs) for performability evaluation is discussed. UltraSAN, a new graphical, X-Windows-based software package that uses SANs, is described. UltraSAN incorporates three innovations: a class of SAN-level performability variables common to both analytical and simulation solution methods, methods that use the performability-variable choice and the SAN structure to greatly reduce the size of the stochastic process required for an analytical solution, and methods that use the performability-variable choice and the SAN structure to reduce the number of activities checked on each state change, thus speeding the simulation. The UltraSAN modeling framework, organization, and user interface are examined. Model construction and solution are described.<<ETX>>Stochastic extensions to Petri nets have received growing attention during the past decade as a model for evaluating the performance, dependability, and performability of computer hardware, software, and networks. Their formal structure permits solution by analytic means in many cases. When this is not possible, they an facilitate the automatic generation of a simulation program to estimate system behavior. The paper describes an X-window based software tool for evaluating systems that are represented as stochastic activity networks, a variant of stochastic Petri nets. The tool, known as UltraSAN, incorporates the results of recent research to significantly reduce the size of the state space that is considered for analytic solution, as well as the number of event types that are considered in simulation. Throughout the paper, a simple local area network model is used to illustrate the concepts, user interface, and model construction and solution methods implemented in the package.<<ETX>>

UltraSAN version 3 overview

UltraSAN is a software package for model-based evaluation of systems represented as stochastic activity networks. The software has been implemented in a modular fashion, with clearly delineated interfaces between model specification, construction, and solution. UltraSAN offers an X Windows-based user interface and both analytical and simulation solution modules for transient and steady-state performance, dependability, and performability measures. Furthermore, the tool facilitates graphical representation of the obtained results by its report generator. This paper gives a very brief overview and pointers to more detailed descriptions of the software.