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Wildland fire prevention and mitigation is of mutual interest to both government and the forest industry. In 1989, the Ontario Ministry of Natural Resources and Forestry introduced the Woods Modification Guidelines that provided rules on how forestry operations should be modified based on local fire danger conditions. Those guidelines were replaced by the Modifying Industrial Operations Protocol (MIOP) in 2008. One objective of MIOP is to allow forestry operations to be done safely for as long as possible as the fire danger increases. We investigate the impacts of these sets of regulations on the frequency of industrial forestry-caused (IDF) wildland fires in the province of Ontario, Canada. Data from 1976 to 2019 are analyzed. A case-crossover study finds no evidence to suggest that MIOP's greater flexibility in operating hours has increased the probability of IDF fire occurrences. This result indicates that MIOP's regulations have had the desired effect of allowing longer working hours on days with heightened fire risk without adding to the seasonal wildland fire load. [ABSTRACT FROM AUTHOR]

We introduce a new approximation procedure to improve the accuracy of matrix analytic methods when using truncated queueing models to analyse infinite buffer systems. This is accomplished through emulating the presence of unobserved waiting customers beyond the finite buffer that are able to immediately enter the system following an observed customer's departure. We show that this procedure results in exact steady-state probabilities at queue lengths below the buffer for truncated versions of the classic M/M/1, M / M / 1 + M , M / M / ∞ , and M/PH/1 queues. We also present two variants of the basic procedure for use within a M / P H / 1 + M queue and a N-queue polling system with exhaustive service, phase-type service and switch-in times, and exponential impatience timers. The accuracy of these two variants in the context of the polling model are compared through several numerical examples. [ABSTRACT FROM AUTHOR]

We analyze a 2-class maintenance system within a single-server polling model framework. There are C + f machines in the system, where C is the cap on the number of machines that can be turned on simultaneously (and hence, be at risk of failure), and the excess f machines comprise a maintenance float which can be used to replace machines that are taken down for repair. The server's behavior is dynamic, capable of switching queues upon a machine failure or service completion depending on both queue lengths. This generalized server behavior permits the analysis of several classic service policies, including preemptive resume priority, non-preemptive priority, and exhaustive. More complicated polices can also be considered, such as threshold-based ones and a version of the Bernoulli service rule. The system is modeled as a level-dependent quasi-birth-and-death process and matrix analytic methods are used to find the steady-state joint queue length distribution, as well as the distribution for the sojourn time of a broken machine. An upper bound on the expected number of working machines as a function of C is derived, and Little's Law is used to find the relationship between the expected number of working machines and the expected sojourn time of a failed machine when f = 0 or f ≥ 1 . Several numerical examples are presented, including how one might optimize an objective function depending on the mean number of working machines, with penalty costs attributed to increasing C or f. [ABSTRACT FROM AUTHOR]

This paper analyzes a 2-class, single-server polling model operating under a ki-limited service discipline with class-dependent switchover times. Arrivals to each class are assumed to follow a Poisson process with phase-type distributed service times. Within each queue, customers are impatient and renege (i.e., abandon the queue) if the time before entry into service exceeds an exponentially distributed patience time. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the per-class waiting time distributions are computed via the use of matrix analytic techniques. The impacts of reneging and choice of service time distribution are investigated through a series of numerical experiments, with a particular focus on the determination of (k1,k2) which minimizes a cost function involving the expected time a customer spends waiting in the queue and an additional penalty cost should reneging take place. [ABSTRACT FROM AUTHOR]