In this work, we consider used coherent systems in the case when the component lifetimes are independent and identically distributed (i.i.d.) with a discrete-time distribution instead of a continuous-time distribution. Then, discrete-time dynamic signature and discrete-time residual signature are proposed for single coherent systems, and discrete-time dynamic joint signature and discrete-time residual joint signature are proposed for two coherent systems with shared components. Associated properties of these proposed discrete-time dynamic signatures are discussed in detail. Some illustrative examples are also presented.
We study the problem of scheduling packets on communication channels whose service availability is modeled by independent Gilbert–Elliot (ON,OFF) Markov chains. Classical models assume that channel states are always known to the scheduler and that transmission is perfect for ON channels. We consider the often more realistic problem of non-preemptive scheduling on imperfect and unobservable channels. In particular, in our model, ON channels have a nonzero probability of unsuccessful transmission, the state of the channel is only observed upon successful transmission, and once a channel is activated, it must remain active until successful transmission. We give conditions under which simple policies are optimal. We also investigate the performance impact of not being able to preempt and of not having access to channel information. Combining known and novel results, we characterize the “Preemption Gain” and “Observability Gain.” Numerically, we show that these gains can be significant, highlighting the critical value of channel state information and preemption, and providing insight into the possible benefit of redesigning systems to permit preemption and/or to provide state information in communication channels.
We consider a cellular network equipped with a retransmission mechanism where the signal transmissions in a single cell depends on interference with simultaneous traffic in surrounding cells. In this framework where failed signals are either retransmitted or lost we study the channel capacity performance of a single-tier model with downlink or uplink traffic. For this purpose, a tractable model that allows for a precise theoretical analysis of coverage probability and coverage rate is developed further. Specifically, we obtain the Shannon capacity in the model and introduce relevant performance measures to guide in the identification of those systems which in a precise sense are able to process all incoming work. To emphasize the generic patterns that arise we extend and simplify the results under a scaling regime of balanced densification, which highlights that performance essentially falls into three categories, for pure-loss, buffered, and no-loss systems.
For some repairable systems, the “initial” failures or defects, if repaired within the specified time period, do not result in the final/functional failures. This can also be interpreted as some time redundancy in various applications. However, with each consecutive repair, this specified time period is usually decreasing, showing a certain deterioration in the quality of repair that can also be interpreted as some imperfectness of repair. On the other hand, the threshold can be fixed, whereas the repair times can be stochastically increasing with each repair. To obtain the corresponding survival probabilities for systems under the described criteria of failures, we employ integral equations of the Volterra type that are solved via the Laplace transforms. The specific cases of exponential distributions of times to defect and repair, and of the geometrically decreasing redundancy time with each repair are considered and analyzed. Provided numerical examples illustrate our findings.
This paper proposes a Palm-based framework for component importance measures conditioned on system failure events, uniformly applicable to nonrepairable, repairable, and phase-mission systems. The formulation does not require renewal, stationary, or Markovian assumptions. We classify measures into transition- and state-based importance. The former captures component failure transitions, recovering Birnbaum and Barlow-Proschan importance, while the latter provides an event-based interpretation of Fussell-Vesely importance. This framework yields well-defined finite-time and phase-conditioned measures for nonstationary systems, establishing a rigorous probabilistic foundation for failure-event-based analysis.
