Waiting time dynamics of priority-queue networks

We study the dynamics of priority-queue networks, generalizations of the binary interacting priority queue model introduced by Oliveira and Vazquez [Physica A {\bf 388}, 187 (2009)]. We found that the original AND-type protocol for interacting tasks is not scalable for the queue networks with loops because the dynamics becomes frozen due to the priority conflicts. We then consider a scalable interaction protocol, an OR-type one, and examine the effects of the network topology and the number of queues on the waiting time distributions of the priority-queue networks, finding that they exhibit power-law tails in all cases considered, yet with model-dependent power-law exponents. We also show that the synchronicity in task executions, giving rise to priority conflicts in the priority-queue networks, is a relevant factor in the queue dynamics that can change the power-law exponent of the waiting time distribution.Comment: 5 pages, 3 figures, minor changes, final published versio

Power series approximations for two-class generalized processor sharing systems

We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are nonempty, a customer of queue 1 is served with probability beta, and a customer of queue 2 is served with probability 1-beta. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating function U(z (1),z (2)) of the stationary queue lengths in terms of a functional equation, and show how to solve this using the theory of boundary value problems. Then, we propose to use the same functional equation to obtain a power series for U(z (1),z (2)) in beta. The first coefficient of this power series corresponds to the priority case beta=0, which allows for an explicit solution. All higher coefficients are expressed in terms of the priority case. Accurate approximations for the mean stationary queue lengths are obtained from combining truncated power series and Pad, approximation

Charging Scheduling of Electric Vehicles with Local Renewable Energy under Uncertain Electric Vehicle Arrival and Grid Power Price

In the paper, we consider delay-optimal charging scheduling of the electric vehicles (EVs) at a charging station with multiple charge points. The charging station is equipped with renewable energy generation devices and can also buy energy from power grid. The uncertainty of the EV arrival, the intermittence of the renewable energy, and the variation of the grid power price are taken into account and described as independent Markov processes. Meanwhile, the charging energy for each EV is random. The goal is to minimize the mean waiting time of EVs under the long term constraint on the cost. We propose queue mapping to convert the EV queue to the charge demand queue and prove the equivalence between the minimization of the two queues' average length. Then we focus on the minimization for the average length of the charge demand queue under long term cost constraint. We propose a framework of Markov decision process (MDP) to investigate this scheduling problem. The system state includes the charge demand queue length, the charge demand arrival, the energy level in the storage battery of the renewable energy, the renewable energy arrival, and the grid power price. Additionally the number of charging demands and the allocated energy from the storage battery compose the two-dimensional policy. We derive two necessary conditions of the optimal policy. Moreover, we discuss the reduction of the two-dimensional policy to be the number of charging demands only. We give the sets of system states for which charging no demand and charging as many demands as possible are optimal, respectively. Finally we investigate the proposed radical policy and conservative policy numerically

The power-series algorithm for Markovian queueing networks

A newversion of the Power-Series Algorithm is developed to compute the steady-state distribution of a rich class of Markovian queueing networks. The arrival process is a Multi-queue Markovian Arrival Process, which is a multi-queue generalization of the BMAP. It includes Poisson, fork and round-robin arrivals. At each queue the service process is a Markovian Service Process, which includes sequences of phase-type distributions, setup times and multi-server queues. The routing is Markovian. The resulting queueing network model is extremely general, which makes the Power-Series Algorithm a useful tool to study load-balancing, capacity-assignment and sequencing problems.Queueing Network;operations research

Cross-Layer Design for Green Power Control

In this work, we propose a new energy efficiency metric which allows one to optimize the performance of a wireless system through a novel power control mechanism. The proposed metric possesses two important features. First, it considers the whole power of the terminal and not just the radiated power. Second, it can account for the limited buffer memory of transmitters which store arriving packets as a queue and transmit them with a success rate that is determined by the transmit power and channel conditions. Remarkably, this metric is shown to have attractive properties such as quasi-concavity with respect to the transmit power and a unique maximum, allowing to derive an optimal power control scheme. Based on analytical and numerical results, the influence of the packet arrival rate, the size of the queue, and the constraints in terms of quality of service are studied. Simulations show that the proposed cross-layer approach of power control may lead to significant gains in terms of transmit power compared to a physical layer approach of green communications.Comment: Presented in ICC 201

Queue Length Asymptotics for Generalized Max-Weight Scheduling in the presence of Heavy-Tailed Traffic

We investigate the asymptotic behavior of the steady-state queue length distribution under generalized max-weight scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic, and the other receives light-tailed traffic. We study the class of throughput optimal max-weight-alpha scheduling policies, and derive an exact asymptotic characterization of the steady-state queue length distributions. In particular, we show that the tail of the light queue distribution is heavier than a power-law curve, whose tail coefficient we obtain explicitly. Our asymptotic characterization also contains an intuitively surprising result - the celebrated max-weight scheduling policy leads to the worst possible tail of the light queue distribution, among all non-idling policies. Motivated by the above negative result regarding the max-weight-alpha policy, we analyze a log-max-weight (LMW) scheduling policy. We show that the LMW policy guarantees an exponentially decaying light queue tail, while still being throughput optimal