16 research outputs found
Exclusive Queueing Process with Discrete Time
In a recent study [C Arita, Phys. Rev. E 80, 051119 (2009)], an extension of
the M/M/1 queueing process with the excluded-volume effect as in the totally
asymmetric simple exclusion process (TASEP) was introduced. In this paper, we
consider its discrete-time version. The update scheme we take is the parallel
one. A stationary-state solution is obtained in a slightly arranged matrix
product form of the discrete-time open TASEP with the parallel update. We find
the phase diagram for the existence of the stationary state. The critical line
which separates the parameter space into the regions with and without the
stationary state can be written in terms of the stationary current of the open
TASEP. We calculate the average length of the system and the average number of
particles
On the speed of convergence to stationarity of the Erlang loss system
We consider the Erlang loss system, characterized by servers, Poisson arrivals and exponential service times, and allow the arrival rate to be a function of We discuss representations and bounds for the rate of convergence to stationarity of the number of customers in the system, and display some bounds for the total variation distance between the time-dependent and stationary distributions. We also pay attention to time-dependent rates
Spatial point process theory
No abstract
Designing a Call Center with Impatient Customers
The most common model to support workforce management of telephone call centers is the M/M/N/B model, in particular its special cases M/M/N (Erlang C, which models out busy signals) and M/M/N/N (Erlang B, disallowing waiting). All of these models lack a central prevalent feature, namely, that impatient customers might decide to leave (abandon) before their service begins. In this paper, we analyze the simplest abandonment model, in which customers' patience is exponentially distributed and the system's waiting capacity is unlimited (M/M/N + M). Such a model is both rich and analyzable enough to provide information that is practically important for call-center managers. We first outline a method for exact analysis of the M/M/N + M model, that while numerically tractable is not very insightful. We then proceed with an asymptotic analysis of the M/M/N + M model, in a regime that is appropriate for large call centers (many agents, high efficiency, high service level). Guided by the asymptotic behavior, we derive approximations for performance measures and propose "rules of thumb" for the design of large call centers. We thus add support to the growing acknowledgment that insights from diffusion approximations are directly applicable to management practice.Tele-Queues, Erlang C, Erlang A, Telephone Call and Contact Centers, Multiserver Exponential Queues, Workforce Management or Staffing, Queues with Abandonment, Diffusion Approxiamtion
Coding and Control for Communication Networks
The purpose of this paper is to survey techniques for constructing effective policies for controlling complex networks, and to extend these techniques to capture special features of wireless communication networks under different networking scenarios. Among the key questions addressed are:
(i) The relationship between static network equilibria, and dynamic network control.
(ii) The effect of coding on control and delay through rate regions.
(iii) Routing, scheduling, and admission control.
Through several examples, ranging from multiple-access systems to network coded multicast, we demonstrate that the rate region for a coded communication network may be approximated by a simple polyhedral subset of a Euclidean space. The polyhedral structure of the rate region, determined by the coding, enables a powerful workload relaxation method that is used for addressing complexity—the relaxation technique provides approximations of a highly complex network by a far simpler one.
These approximations are the basis of a specific formulation of an h-MaxWeight policy for network routing. Simulations show a 50% improvement in average delay performance as compared to methods used in current practice.National Science Foundation (U.S.) (Grant ECS- 0523620)United States. Defense Advanced Research Projects Agency. Information Theory for Mobile Ad-Hoc Networks Progra