Social networking has been a feature of human society. From the early hunter-gatherer tribes, medieval guilds, the twentieth century workplaces, up to online entities like Facebook and Twitter, it is difficult to think of a time or place where all people did not belong to at least one cooperative group. It follows that social network formation has been studied extensively in the past decades and will continue to be a popular area of research. Past research has primarily confined itself to considering cases in which new members are introduced into the networks by making a constant number of connections to those who are already present in the networks. Our study aims to fill the glaring gap in the variety of network formation modelling. Most notably, we want to consider scenarios in which the number of connections new members make to those already present in the networks is determined by chance. More specifically, the number of connections made to existing members when a new one is introduced into the network is characterized by a positive integer-valued random variable. The objective of the study is to determine the distribution of degree of a node in this kind of social networks. It is determined that the node degree distribution is a mixture of geometric distributions. Three numerical examples are provided in the study to demonstrate the validity of our findings.
Healthcare currently consumes 17% of the U.S. Gross Domestic Product and is expected to reach 20% within the coming decade. Confronted with such high costs, sharp demand, and limited capacity, many hospitals now are vying for shorter lengths of stay and are transferring services from inpatient to outpatient facilities. This paper seeks to develop a methodology for constructing effective outpatient appointment scheduling systems. The objective of these appointment systems is to minimize the average total cost function describing total costs incurred by patient waiting and by staff idle time and overtime. In the paper, we will establish that the average total cost function exhibits a unimodal curve. The lowest point of the curve essentially means the lowest average total cost. We will next develop a simulation-based heuristic algorithm for finding an outpatient schedule near the lowest point. In the paper, we present numerical examples using the heuristic based upon a set of predetermined unit costs. Specifically, we find the near optimal interappointment times for schedules, where there are two and three patients in each block, respectively. The current work does not consider possible no shows and walk-ins. Future work will undertake these issues. 9
In this paper, we look into a novel notion of the standard M/M/1 queueing system. In our study, we assume that there is a single server and that there are two types of customers: real and imaginary customers. Real customers are regular customers arriving into our queueing system in accordance with a Poisson process. There exist infinitely many imaginary customers residing in the system. Real customers have service priority over imaginary customers. Thus, the server always serves real (regular) customers one by one if there are real customers present in the system. After serving all real customers, the server immediately serves, one at a time, imaginary customers residing in the system. A newly arriving real customer presumably does not preempt the service of an imaginary customer and hence must wait in the queue for their service. The server immediately serves a waiting real customer upon service completion of the imaginary customer currently under service. All service times are identically, independently, and exponentially distributed. Since our systems are characterized by continuous service by the server, we dub our systems continuous-service M/M/1 queueing systems. We conduct the steady-state analysis and determine common performance measures of our systems. In addition, we carry out simulation experiments to verify our results. We compare our results to that of the standard M/M/1 queueing system, and draw interesting conclusions.
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