Distributed State Space Generation of Discrete-State Stochastic Models

High-level formalisms such as stochastic Petri nets can be used to model complex systems. Analysis of logical and numerical properties of these models often requires the generation and storage of the entire underlying state space. This imposes practical limitations on the types of systems which can be modeled. Because of the vast amount of memory consumed, we investigate distributed algorithms for the generation of state space graphs. The distributed construction allows us to take advantage of the combined memory readily available on a network of workstations. The key technical problem is to find effective methods for on-the-fly partitioning, so that the state space is evenly distributed among processors. In this paper we report on the implementation of a distributed state space generator that may be linked to a number of existing system modeling tools. We discuss partitioning strategies in the context of Petri net models, and report on performance observed on a network of workstations, as well as on a distributed memory multi-computer. Discrete-state models are a valuable tool in the representation, design, and analysis of computer and communication systems, both hardware and software. We are particularly interested in stochastic formalisms, where some probability distribution is associated with the possible events in each state, so that the model implicitly defines a stochastic process. These are then used to carry on performance, reliability, or performability studies. Most real systems, however, exhibit complex behaviors which cannot be captured by simple models having a small or regular state space. Given the high expressive power of formalisms such as Petri nets [24, 23], queueing networks, state charts [17], and ad hoc textual languages [14], the correct logical behavior can, in principle, be modeled exactly. The timing behavior is then defined by associating a probability distribution to the duration of each activity. The resulting stochastic process can be solved by discrete-event simulation. However, if the distributions are restricted to be either exponential or geometric, the process is a continuoustime Markov chain (CTMC) or a discrete-time Markov chain (DTMC), respectively, and can be solved numerically. We focus on the CTMC case, where, with the exception of very special circumstances such as the existence of product-form solutions [3, 26] or of extensive symmetries [5, 13], the numerical solution requires the generation and storage of the entire state space. This is the main