Decomposition of network of queues with self-similar traffic

Jackson's network of queues model greatly simplifies the performance analysis of telecommunication networks with Poisson traffic arrivals and exponential service times. It reduces the analysis of a network into the analysis of individual communication links, each of which may be modeled as an M/M/m queue. Motivated by the growing significance of self-similar traffic in modeling broadband network traffic, we propose a new network of queues model for telecommunication networks. Our model resembles Jackson's model except that the arrival is self-similar and the service time is deterministic. It captures the characteristics of modern high speed cell-based networks. We hypothesize a result analogous to Jackson's Theorem, that each mode of this network model behaves as a G/D/1 queue with self-similar arrival. Based on this hypothesis, many network-wide performance measures, such as the end-to-end delay, can be evaluated in a simple fashion. Our hypothesis is strongly supported by three facts, namely, the sum of independent self-similar processes, the random splitting of self-similar processes, and the output process of a deterministic service time queue with self-similar input are all self-similar.published_or_final_versio

Decomposition of network of queues with self-similar traffic

Jackson's network of queues model greatly simplifies the performance analysis of telecommunication networks with Poisson traffic arrivals and exponential service times. It reduces the analysis of a network into the analysis of individual communication links, each of which may be modeled as an M/M/m queue. Motivated by the growing significance of self-similar traffic in modeling broadband network traffic, we propose a new network of queues model for telecommunication networks. Our model resembles Jackson's model except that the arrival is self-similar and the service time is deterministic. It captures the characteristics of modern high speed cell-based networks. We hypothesize a result analogous to Jackson's Theorem, that each mode of this network model behaves as a G/D/1 queue with self-similar arrival. Based on this hypothesis, many network-wide performance measures, such as the end-to-end delay, can be evaluated in a simple fashion. Our hypothesis is strongly supported by three facts, namely, the sum of independent self-similar processes, the random splitting of self-similar processes, and the output process of a deterministic service time queue with self-similar input are all self-similar.published_or_final_versio

Low-Latency Millimeter-Wave Communications: Traffic Dispersion or Network Densification?

This paper investigates two strategies to reduce the communication delay in future wireless networks: traffic dispersion and network densification. A hybrid scheme that combines these two strategies is also considered. The probabilistic delay and effective capacity are used to evaluate performance. For probabilistic delay, the violation probability of delay, i.e., the probability that the delay exceeds a given tolerance level, is characterized in terms of upper bounds, which are derived by applying stochastic network calculus theory. In addition, to characterize the maximum affordable arrival traffic for mmWave systems, the effective capacity, i.e., the service capability with a given quality-of-service (QoS) requirement, is studied. The derived bounds on the probabilistic delay and effective capacity are validated through simulations. These numerical results show that, for a given average system gain, traffic dispersion, network densification, and the hybrid scheme exhibit different potentials to reduce the end-to-end communication delay. For instance, traffic dispersion outperforms network densification, given high average system gain and arrival rate, while it could be the worst option, otherwise. Furthermore, it is revealed that, increasing the number of independent paths and/or relay density is always beneficial, while the performance gain is related to the arrival rate and average system gain, jointly. Therefore, a proper transmission scheme should be selected to optimize the delay performance, according to the given conditions on arrival traffic and system service capability

Dynamic Vehicle Routing for Data Gathering in Wireless Networks

We consider a dynamic vehicle routing problem in wireless networks where messages arriving randomly in time and space are collected by a mobile receiver (vehicle or a collector). The collector is responsible for receiving these messages via wireless communication by dynamically adjusting its position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the delay performance in such networks. We show that the necessary and sufficient condition for the stability of such a system (in the bounded average number of messages sense) is given by {\rho}<1 where {\rho} is the average system load. We derive fundamental lower bounds for the delay in the system and develop policies that are stable for all loads {\rho}<1 and that have asymptotically optimal delay scaling. Furthermore, we extend our analysis to the case of multiple collectors in the network. We show that the combination of mobility and wireless transmission results in a delay scaling of {\Theta}(1/(1- {\rho})) with the system load {\rho} that is a factor of {\Theta}(1/(1- {\rho})) smaller than the delay scaling in the corresponding system where the collector visits each message location.Comment: 19 pages, 7 figure