No abstract

This paper studies inspected systems with non-self-announcing failures where the rate of deterioration is governed by a Markov chain. We compute the lifetime distribution and availability when the system is inspected according to a periodic inspection policy. In doing so, we expose the role of certain transient distributions of the environment.

This note examines estimation of the traffic intensity in an M/G/1 queue. We show that the ratio of sample mean service times to the sample mean interarrival times has undesirable sampling properties. To remedy this, two alternative estimators are introduced.

No abstract

In this paper we identify a monotonicity in all countable-state-space reversible Markov chains and examine several consequences of this structure. In particular, we show that the return times to every state in a reversible chain have a decreasing hazard rate on the subsequence of even times. This monotonicity is used to develop geometric convergence rate bounds for time-reversible Markov chains. Results relating the radius of convergence of the probability generating function of first return times to the chain's rate of convergence are presented. An effort is made to keep the exposition rudimentary.

This paper studies inspected systems with non-self-announcing failures where the rate of deterioration is governed by a Markov chain. We compute the lifetime distribution and availability when the system is inspected according to a periodic inspection policy. In doing so, we expose the role of certain transient distributions of the environment.

No abstract

We show for the three-node Jackson network studied in [3] that a customer’s sojourn times in nodes 1 and 3 are positively correlated. We actually prove a stronger result, that the two sojourn times are associated random variables. Our proof uses a stochastic ordering argument similar to that in [4].