The effect of signals on stability, stable throughput region, and delay in a two-user slotted ALOHA-based random-access system with collisions is considered. This work gives rise to the development of random access G-networks, which can model security attacks, expiration of deadlines, or other malfunctions, and introduce load balancing among highly interacting queues. The users are equipped with infinite capacity buffers accepting external bursty arrivals. We consider both negative and triggering signals. Negative signals delete a packet from a user queue, while triggering signals cause the instantaneous transfer of packets among user queues. We obtain the exact stability region, and show that the stable throughput region is a subset of it. Moreover, we perform a compact mathematical analysis to obtain exact expressions for the queueing delay by solving a non-homogeneous Riemann boundary value problem. A computationally efficient way to obtain explicit bounds for the expected number of buffered packets at user queues is also presented. The theoretical findings are numerically evaluated and insights regarding the system performance are derived.

We use the Energy Packet Network (EPN) to investigate an optimal energy distribution problem for the computer-communication system which is powered by intermittent renewable energy sources. The objective is to find an optimal energy distribution to minimize the proposed cost function which computes penalty costs caused by the overall average response time of jobs and the energy loss. In this EPN system, we consider the energy can be lost through storage leakages, or due to empty workstations which will consume energy even no job needs to be processed. Related numerical examples with different sets of parameter values are presented in the paper to evaluate the system performance and to examine the obtained analytical solution. Then a special case is considered to study the optimal system performance when the total energy harvesting rate is sufficiently large.

This paper introduces a special issue of this journal (Probability in the Engineering and Informational Sciences) that is devoted to G(elenbe)-Networks and their Applications. The special issue is based on revised versions of some of the papers that were presented at a workshop held in early January 2017 at the Séminaire Saint-Paul in Nice (France). It includes contributions in several research directions that followed from the introduction of the G-Network in the late 1980s. The papers present original theoretical developments, as well as applications of G-Networks to Machine Learning, to the performance optimization of energy systems via the novel Energy Packet Networks formalism for systems that operate with renewable and intermittent energy sources, and to packet network routing and Cloud management over the Internet. We introduce these contributions from the perspective of an overview of recent work based on G-Networks.

Single server queues with repeated attempts are useful inthe modeling of computer and telecommunication systems. In addition, weconsider in this paper the possibility of disasters. When a disasteroccurs, all the customers present in the system are destroyedimmediately. Using a regenerative approach, we derive a numericallystable recursion scheme for the state probabilities. This model can beemployed to analyze the behaviour of a buffer in computers with virusinfections.

We derive expressions for the generating function of the equilibrium queue length probability distribution in a single server queue with general service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. For the case of first come first served queueing discipline for the positive customers, we compare the killing strategies in which either the last customer in the queue or the one in service is removed by a negative customer. We then consider preemptive-restart with resampling last come first served queueing discipline for the positive customers, combined with the elimination of the customer in service by a negative customer—the case of elimination of the last customer yields an analysis similar to first come first served discipline for positive customers. The results show different generating functions in contrast to the case where service times are exponentially distributed. This is also reflected in the stability conditions. Incidently, this leads to a full study of the preemptive-restart with resampling last come first served case without negative customers. Finally, approaches to solving the Fredholm integral equation of the first kind which arises, for instance, in the first case are considered as well as an alternative iterative solution method.

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.