Queues and risk models with simultaneous arrivals

We focus on a particular connection between queueing and risk models in a multi-dimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case that the service times are ordered (from largest in the first queue to smallest in the last queue) we obtain the Laplace-Stieltjes transform of the joint stationary workload distribution. Using a multivariate duality argument between queueing and risk models, this also gives the Laplace transform of the survival probability of all books in a multivariate risk model with simultaneous claim arrivals and the same ordering between claim sizes. Other features of the paper include a stochastic decomposition result for the workload vector, and an outline how the two-dimensional risk model with a general two-dimensional claim size distribution (hence without ordering of claim sizes) is related to a known Riemann boundary value problem

Scalability analysis of large-scale LoRaWAN networks in ns-3

As LoRaWAN networks are actively being deployed in the field, it is important to comprehend the limitations of this Low Power Wide Area Network technology. Previous work has raised questions in terms of the scalability and capacity of LoRaWAN networks as the number of end devices grows to hundreds or thousands per gateway. Some works have modeled LoRaWAN networks as pure ALOHA networks, which fails to capture important characteristics such as the capture effect and the effects of interference. Other works provide a more comprehensive model by relying on empirical and stochastic techniques. This work uses a different approach where a LoRa error model is constructed from extensive complex baseband bit error rate simulations and used as an interference model. The error model is combined with the LoRaWAN MAC protocol in an ns-3 module that enables to study multi channel, multi spreading factor, multi gateway, bi-directional LoRaWAN networks with thousands of end devices. Using the lorawan ns-3 module, a scalability analysis of LoRaWAN shows the detrimental impact of downstream traffic on the delivery ratio of confirmed upstream traffic. The analysis shows that increasing gateway density can ameliorate but not eliminate this effect, as stringent duty cycle requirements for gateways continue to limit downstream opportunities.Comment: 12 pages, submitted to the IEEE Internet of Things Journa

Towards a System Theoretic Approach to Wireless Network Capacity in Finite Time and Space

In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends itself to conservative numerical results in finite regimes. To properly account for queueing behavior beyond a simple calculus based on average rates, we advocate a system theoretic methodology for the capacity problem in finite time and space regimes. This methodology also accounts for spatial correlations arising in networks with CSMA/CA scheduling and it delivers rigorous closed-form capacity results in terms of probability distributions. Unlike numerous existing asymptotic results, subject to anecdotal practical concerns, our transient one can be used in practical settings: for example, to compute the time scales at which multi-hop routing is more advantageous than single-hop routing

Model checking medium access control for sensor networks

We describe verification of S-MAC, a medium access control protocol designed for wireless sensor networks, by means of the PRISM model checker. The S-MAC protocol is built on top of the IEEE 802.11 standard for wireless ad hoc networks and, as such, it uses the same randomised backoff procedure as a means to avoid collision. In order to minimise energy consumption, in S-MAC, nodes are periodically put into a sleep state. Synchronisation of the sleeping schedules is necessary for the nodes to be able to communicate. Intuitively, energy saving obtained through a periodic sleep mechanism will be at the expense of performance. In previous work on S-MAC verification, a combination of analytical techniques and simulation has been used to confirm the correctness of this intuition for a simplified (abstract) version of the protocol in which the initial schedules coordination phase is assumed correct. We show how we have used the PRISM model checker to verify the behaviour of S-MAC and compare it to that of IEEE 802.11