Structural factoring approach for analyzing stochastic networks

The problem of finding the distribution of the shortest path length through a stochastic network is investigated. A general algorithm for determining the exact distribution of the shortest path length is developed based on the concept of conditional factoring, in which a directed, stochastic network is decomposed into an equivalent set of smaller, generally less complex subnetworks. Several network constructs are identified and exploited to reduce significantly the computational effort required to solve a network problem relative to complete enumeration. This algorithm can be applied to two important classes of stochastic path problems: determining the critical path distribution for acyclic networks and the exact two-terminal reliability for probabilistic networks. Computational experience with the algorithm was encouraging and allowed the exact solution of networks that have been previously analyzed only by approximation techniques

Computing the periodicity of finite Markov chains

Determining the period of a finite irreducible Markov chains involves finding the greatest common divisor of the number of transitions that carry any state back to itself with non-zero probability. This is equivalent to finding the greatest common divisor of the lengths of all cycles in the directed graph defined by the state transition diagram. A linear-time algorithm based on a breadth-first search of this directed graph can be used to determine the period of the chain without examining all cycles in the graph

An algorithm for approximating the performance of telecommunication systems

A problem encountered in the analysis of telecommunication systems, as well as in other distribution systems, is that of estimating the performance level of the system in meeting user demands with available resources. In particular, the user demands and the available resources are only assumed to be known stochastically, and communication links may operate at various levels. This situation can be modeled as a stochastic network flow problem, in which each edge of the network assumes a finite number of values (corresponding to different capacity levels) with known probabilities. In each state of the network, there are deterministic supplies, demands, and link capacities, and we are interested in whether overall demand can be met using the present supply of resources. If not, we are interested in the maximum demand that can be met using the best allocation of flows. The approach used here to estimate the probability of unmet demand, as well as the average unmet demand, involves generating only "high leverage" states of the system──states having high probability and/or high values of unmet demand. A new method is proposed for generating such states and producing bounds on various performance measures for the system

Development and implementation of an online clinical pathway for adult chronic kidney disease in primary care: a mixed methods study

Abstract Background Primary care physicians and other primary health care professionals from Alberta, Canada identified a clinical pathway as a potential tool to facilitate uptake of clinical practice guidelines for the diagnosis, management and referral of adults with chronic kidney disease. We describe the development and implementation of a chronic kidney disease clinical pathway (CKD-CP; www.ckdpathway.ca ). Methods The CKD-CP was developed and implemented based on the principles of the Knowledge-To-Action Cycle framework. We used a mixed methods approach to identify the usability and feasibility of the CKD-CP. This included individual interviews, an online survey and website analytics, to gather data on barriers and facilitators to use, perceived usefulness and characteristics of users. Results are reported using conventional qualitative content analysis and descriptive statistics. Results Eighteen individual interviews were conducted with primary care physicians, nephrologists, pharmacists and nurse practitioners to identify themes reflecting both barriers and facilitators to integrating the CKD-CP into clinical practice. Themes identified included: communication, work efficiency and confidence. Of the 159 participants that completed the online survey, the majority (52 %) were first time CKD-CP users. Among those who had previously used the CKD-CP, 94 % agreed or strongly agreed that the pathway was user friendly, provided useful information and increased their knowledge and confidence in the care of patients with CKD. Between November 2014 and July 2015, the CKD-CP website had 10,710 visits, 67 % of which were new visitors. The 3 most frequently visited web pages were home, diagnose and medical management. Canada, Indonesia and the United States were the top 3 countries accessing the website during the 9 month period. Conclusions An interactive, online, point-of-care tool for primary care providers can be developed and implemented to assist in the care of patients with CKD. Our findings are important for making refinements to the CKD –CP website via ongoing discussions with end-users and the development team, along with continued dissemination using multiple strategies