Level product form QSF processes and an analysis of queues with Coxian interarrival distribution

In this article, we study a class of Quasi‐Skipfree (QSF) processes where the transition rate submatrices in the skipfree direction have a column times row structure. Under homogeneity and irreducibility assumptions we show that the stationary distributions of these processes have a product form as a function of the level. For an application, we will discuss the ‐queue that can be modeled as a QSF process on a two‐dimensional state space. In addition, we study the properties of the stationary distribution and derive monotonicity of the mean number of the customers in the queue, their mean sojourn time and the variance as a function of for fixed mean arrival rate. © 2016 Wiley Periodicals, Inc. Naval Research Logisticsxs 66:57–72, 2019     

General Zuo’s counter-insurgency doctrine

ABSTRACT

This paper examines the career of one of the most notable of Chinese state officials in the mid-nineteenth century, General Zuo Zongtang (1812–1885) at a time when the Qing Empire was beset by enemies on all sides along with the massive Taiping Rebellion (1851–65). The paper explores how Zuo created a coherent and flexible counter-insurgency doctrine that underpinned his suppression of the Taipings, the Nian, Muslim rebels of the northwest and the defeat of a massive Sufi revolt in Central Asia. The paper also shows how Zuo helped convince the Russians to return territory they occupied in Central Asia, thereby preserving the territorial integrity of the Qing Empire in the region.