RESUMO
Mean-field approximation is a method to investigate the behavior of stochastic models formed by a large number of interacting objects. A new approximation was recently established, i.e., the refined mean-field approximation, and its high accuracy when the number of objects is small has been shown. In this work, we consider the model of the 802.11 protocol, which is a discrete-time model and show how the refined mean-field approximation can be adapted to this model. Our results confirm the accuracy of the refined mean-field approximation when the model with N objects is in discrete time.
RESUMO
Size-based routing policies are known to perform well when the variance of the distribution of the job size is very high. We consider two size-based policies in this paper: Task Assignment with Guessing Size (TAGS) and Size Interval Task Assignment (SITA). The latter assumes that the size of jobs is known, whereas the former does not. Recently, it has been shown by our previous work that when the ratio of the largest to shortest job tends to infinity and the system load is fixed and low, the average waiting time of SITA is, at most, two times less than that of TAGS. In this article, we first analyze the ratio between the mean waiting time of TAGS and the mean waiting time of SITA in a non-asymptotic regime, and we show that for two servers, and when the job size distribution is Bounded Pareto with parameter α=1, this ratio is unbounded from above. We then consider a system with an arbitrary number of servers and we compare the mean waiting time of TAGS with that of Size Interval Task Assignment with Equal load (SITA-E), which is a SITA policy where the load of all the servers are equal. We show that in the light traffic regime, the performance ratio under consideration is unbounded from above when (i) the job size distribution is Bounded Pareto with parameter α=1 and an arbitrary number of servers as well as (ii) for Bounded Pareto distributed job sizes with α∈(0,2)\{1} and the number of servers tends to infinity. Finally, we use the result of our previous work to show how to design decentralized systems with quality of service constraints.
RESUMO
Motivated by current communication networks in which users can choose different transmission channels to operate and also by the recent growth of renewable energy sources, we study the average Age of Information of a status update system that is formed by two parallel homogeneous servers and such that there is an energy source that feeds the system following a random process. An update, after getting service, is delivered to the monitor if there is energy in a battery. However, if the battery is empty, the status update is lost. We allow preemption of updates in service and we assume Poisson generation times of status updates and exponential service times. We show that the average Age of Information can be characterized by solving a system with eight linear equations. Then, we show that, when the arrival rate to both servers is large, the average Age of Information is one divided by the sum of the service rates of the servers. We also perform a numerical analysis to compare the performance of our model with that of a single server with energy harvesting and to study in detail the aforementioned convergence result.
RESUMO
We investigate a system with Poisson arrivals to two queues. One queue stores the status updates of the process of interest (or data packets) and the other handles the energy that is required to deliver the updates to the monitor. We consider that the energy is represented by packets of discrete unit. When an update ends service, it is sent to the energy queue and, if the energy queue has one packet, the update is delivered successfully and the energy packet disappears; however, in case the energy queue is empty, the update is lost. Both queues can handle, at most, one packet and the service time of updates is exponentially distributed. Using the Stochastic Hybrid System method, we characterize the average Age of Information of this system. Due to the difficulty of the derived expression, we also explore approximations of the average Age of Information of this system.