No abstract

We examine the problem of optimally maintaining a stochastically degrading system using preventive and reactive replacements. The system's rate of degradation is modulated by an exogenous stochastic environment process, and the system fails when its cumulative degradation level first reaches a fixed deterministic threshold. The objective is to minimize the total expected discounted cost of preventively and reactively replacing such a system over an infinite planning horizon. To this end, we present and analyze a Markov decision process model. It is shown that, for each environment state, there exists an optimal threshold-type replacement policy. Additionally, empirical evidence suggests that, when the environment process is monotone, and the state-dependent degradation rates are totally ordered, the optimal threshold is monotone. Lastly, we derive closed-form bounds on the optimal thresholds.

No abstract

No abstract

This article describes the M / M / s queueing system, or Erlang delay model, which is a stochastic service system with a Poisson arrival process and s (1 ≤  s  < ∞) independent and identical servers, each of which serves customers in an exponentially distributed amount of time. Arriving customers join an infinite queue if they find all of the s servers busy. The main purpose of this article is to summarize the characteristics of the M / M / s system, namely the steady‐state probability distribution of the number of customers in the system, the steady‐state performance parameters, and steady‐state delay probability which is computed using the well‐known Erlang C formula. As a special case of the M / M / s system, we also discuss the M / M / s / c queue. Computational issues and some structural properties of the Erlang C formula are also discussed.

Purpose This paper aims to examine the per capita income convergence of 57 member countries of the Organization of Islamic Cooperation (OIC) over the period 1990–2017 and to investigate the determinants of convergence club formations. Design/methodology/approach The authors applied the methodology of Phillips and Sul (2007, 2009) to identify the convergence clubs and estimated several-ordered logit models to determine the key drivers. Findings The results support existence of two convergence clubs and one diverging unit, indicating that 30 and 26 member countries form two separate groups converging to their own steady-state paths. They also suggest a significant productivity divergence between these clubs. The authors showed that the number of convergence clubs started to decline after the global financial crisis in 2008. Moreover, they found that fixed capital formation, education and political stability are key drivers of convergence club membership. Practical implications There is a strong need for large-scale policy interventions to close the gap between leading and lagging clubs of the OIC. A substantial investment in human and physical capital seems necessary for lower-income OIC countries. Originality/value This is the first empirical study on the existence of convergence clubs among member countries of the OIC.

No abstract