In this paper, we show the structural characteristics that a particular class of generalized stochastic Petri nets must exhibit in order for their stationary probabilities to have a product-form. Sufficient conditions for identifying such a class are derived and proven with the development of a series of transformations that can also be used to construct, for any GSPN of the class, an equivalent SPN. These resulting SPNs represent the structures that can be analyzed with standard methods for product-form SPNs to establish whether the original GSPNs have product-form solutions and to compute their performance indices with effective approaches based on computationally efficient algorithms that avoid the generation of their underlying state spaces.

Locating a center or a median in a graph is a fundamental graph-theoretic problem. Centers and medians are especially important in distributed systems because they are ideal locations for placing resources that need to be shared among different processes in a network. This paper presents simple self-stabilizing algorithms for locating centers and medians of trees. Since these algorithms are self-stabilizing, they can tolerate transient failures. In addition, they can automatically adjust to a dynamically changing tree topology. After the algorithms are presented, their correctness is proven and upper bounds on their time complexity are established. Finally, extensions of our algorithms to trees with arbitrary, positive edge costs are sketched.

No abstract available.

We consider a particular class of Stochastic Petri Nets whose stationary probabilities at arbitrary instants exhibit a product form. We study these nets at specific instants in the steady state that occur directly after the firing of a transition. We focus our attention on the instant after tokens are removed from the places specified by a transition's input bag and just before tokens are entered into the places specified by the same transition's output bag. We show that the stationary probabilities at “arrival instants” are related to corresponding stationary probabilities at arbitrary instants in net(s) with lower load. We then show how one of the “arrival” theorems can be applied to the derivation of a formula for the mean sojourn time of a token in a place at steady state. This is the basis for the development of a Mean Value Analysis algorithm for the computation of performance indices for Product-Form Stochastic Petri Nets.

A colored generalized stochastic Petri net (CGSPN) model was used to study the correctness and performance of the Lamport concurrent algorithm to solve the mutual exclusion problem on machines lacking an atomic test and set instruction. In particular, a parametric formal proof of liveness is developed based on the structure and initial state of the model. The performance evaluation is based on a Markovian analysis that exploits the symmetries of the model to reduce the cost of the numerical solution. Both kinds of analysis are supported by efficient algorithms. The potential of the GSPN modeling technique is illustrated on an academic but nontrivial example of an application from distributed systems.>

Database designers and researchers often need efficient schemes to evaluate transaction performance. In this paper, we chose two important performance measures: the average number of nodes accessed and the average number of data items accessed per node by a transaction in a distributed database system. We derive analytical expressions to evaluate these metrics. For general applicability, we consider partially replicated distributed database systems. Our first set of analytic results are closed-form expressions for these two measures. These are based on some fairly restrictive simplifying assumptions. When these assumptions are relaxed, no closed-form expressions exist for these averages. Hence, we develop an efficient algorithm to compute these averages.

An O(n/sup 2/) heuristic algorithm using randomized decisions is developed for determining a near-optimal set of nodes. For small values of n, the authors can determine how close the heuristic solution is to the optimal set of nodes. They also compare their heuristic to other algorithms reported in the literature.>

A technique is presented whereby queueing network models and generalized stochastic Petri nets are combined in such a way as to exploit the best features of both modeling techniques. The resulting hierarchical modeling approach is useful in the solution of complex models of system behavior. The authors have chosen two examples from the recent literature to illustrate the power and scope of this technique. They also demonstrate how folding of the generalized stochastic Petri net models for these two examples is useful in obtaining efficiently solvable, approximate models (bounding models).>

In a recent paper, Lam and Lien described an algorithm called tree-convolution that can reduce the space and computation time required for evaluating sparse multiclass, product-form queueing networks. In this paper, we develop an exact algorithm based on mean value analysis (MVA) that is the counterpart of the tree-convolution algorithm. The order of reduction in storage and computation achieved by our new Tree-MVA algorithm compared to the standard MVA algorithm is the same order of reduction obtained by the tree-convolution algorithm over that of the standard convolution algorithm. Our Tree-MVA algorithm preserves the inherent simplicity of MVA based algorithms.

Much work has been done on the modeling of hardware resources; far fewer studies have been conducted on the impact of software systems on the underlying hardware. The authors address one such case in which blocking is present because of critical sections of code; this cannot be treated within the framework of product-form queuing network models. They show how a combination of generalized stochastic petri nets and queuing networks can easily model the situation under consideration. In addition, they show how a simple extension of this model can be applied to studying realistic systems with several domains.

We develop Generalized Stochastic Petri Net models for several priority queueing disciplines. The building blocks of these models are explained and many variants are easily derivable from them. We then combine these building blocks with product-form queueing network models. Numerical results are provided that illustrate the effectiveness of the method.

We describe a new technique for accessing a shared bus in a distributed computing environment. The load balancing bus accessing scheme can be modeled by a new station type that can be incorporated in a BCMP multiple class queueing network model of the distributed system. We show one simple means of implementing the load balancing scheme.

Consider a queueing system in which customers (or jobs) arrive to one of Q separate queues to await service from one of S identical servers (Figure 1). Once a job enters a queue it does not leave that queue until it has been selected for service. Any server can serve any job from any queue. A job selected for service cannot be preempted. In this paper we consider jobs to be in a single class; for the multiple class result see [AFSH81a]. We assume once a queue has been selected, job scheduling from that queue is fair. In particular, our results hold for first come first serve as well as random selection [SPIR79] and, for that matter, any fair nonpreemptive scheduling policy within a queue. We assume that arrivals to each queue follow a Poisson process with the mean arrival rate to queue q being λq. The S identical exponential servers are each processing work at a mean rate of μ.