Random Fluid Limit of an Overloaded Polling Model

In the present paper, we study the evolution of an overloaded cyclic polling model that starts empty. Exploiting a connection with multitype branching processes, we derive fluid asymptotics for the joint queue length process. Under passage to the fluid dynamics, the server switches between the queues infinitely many times in any finite time interval causing frequent oscillatory behavior of the fluid limit in the neighborhood of zero. Moreover, the fluid limit is random. Additionally, we suggest a method that establishes finiteness of moments of the busy period in an M/G/1 queue.Comment: 36 pages, 2 picture

Fluid limit of a PS-queue with multistage service

We consider a variation of the processor-sharing (PS) queue, inspired by freelance job websites where multiple freelancers compete for a single job. We develop fluid limit approximations for the overloaded PS-model with multiple (possibly infinitely many) service stages. Based on this approximation, we estimate what proportion of freelancers get the job they apply for. In addition, the PS model studied here is an instance of PS with routing and impatience, for which no Lyapunov function is known, and we suggest some partial solutions

Fluid limit of a PS-queue with multistage service

\u3cp\u3eWe consider a variation of the processor-sharing (PS) queue, inspired by freelance job websites where multiple freelancers compete for a single job. We develop fluid limit approximations for the overloaded PS-model with multiple (possibly infinitely many) service stages. Based on this approximation, we estimate what proportion of freelancers get the job they apply for. In addition, the PS model studied here is an instance of PS with routing and impatience, for which no Lyapunov function is known, and we suggest some partial solutions.\u3c/p\u3

Fluid approximation of a call center model with redials and reconnects

In many call centers, callers may call multiple times. Some of the calls are re-attempts after abandonments (redials), and some are re-attempts after connected calls (reconnects). The combination of redials and reconnects has not been considered when making staffing decisions, while not distinguishing them from the total calls will inevitably lead to under- or overestimation of call volumes, which results in improper and hence costly staffing decisions. Motivated by this, in this paper we study call centers where customers can abandon, and abandoned customers may redial, and when a customer finishes his conversation with an agent, he may reconnect. We use a fluid model to derive first order approximations for the number of customers in the redial and reconnect orbits in the heavy traffic. We show that the fluid limit of such a model is the unique solution to a system of three differential equations. Furthermore, we use the fluid limit to calculate the expected total arrival rate, which is then given as an input to the Erlang A formula for the purpose of calculating the service levels and abandonment probabilities. The performance of such a procedure is validated numerically in the case of both single intervals with constant parameters and multiple intervals with time-dependent parameters. The results demonstrate that this approximation method leads to accurate estimations for the service levels and the abandonment probabilities. Keywords: Call centers; Fluid model; Redial; Reconnect; Erlang