2 research outputs found
Spare parts provisioning for multiple k-out-of-n:G systems
In this paper, we consider a repair shop that fixes failed components from different k-out-of-n:G systems. We assume that each system consists of the same type of component; to increase availability, a certain number of components are stocked as spare parts. We permit a shared inventory serving all systems and/or reserved inventories for each system; we call this a hybrid model. Additionally, we consider two alternative dispatching rules for the repaired component. The destination for a repaired component can be chosen either on a first-come-first-served basis or by following a static priority rule. Our analysis gives the steady-state system size distribution of the two alternative
models at the repair shop. We conduct numerical examples minimizing the spare parts held while subjecting the availability of each system to exceed a targeted value. Our findings show that unless the availabilities of systems are close, the HP policy is better than the HF policy
Stationary analysis of a single queue with remaining service time dependent arrivals
We study a generalization of the system (denoted by ) with
independent and identically distributed (iid) service times and with an arrival
process whose arrival rate depends on the remaining service
time of the current customer being served. We derive a natural stability
condition and provide a stationary analysis under it both at service completion
times (of the queue length process) and in continuous time (of the queue length
and the residual service time). In particular, we show that the stationary
measure of queue length at service completion times is equal to that of a
corresponding system. For we show that the continuous time
stationary measure of the system is linked to the system via a
time change. As opposed to the queue, the stationary measure of queue
length of the system at service completions differs from its marginal
distribution under the continuous time stationary measure. Thus, in general,
arrivals of the system do not see time averages. We derive formulas
for the average queue length, probability of an empty system and average
waiting time under the continuous time stationary measure. We provide examples
showing the effect of changing the reshaping function on the average waiting
time.Comment: 31 pages, 3 Figure