arXiv subjects

Ioannis Dimitriou

Publications and source records attributed to Ioannis Dimitriou.

22 records · Page 2Linked to original sources

arXiv2018

On the power series approximations of a structured batch arrival two-class retrial system with weighted fair orbit queues

We provide power series approximations for a structured batch arrival single server retrial system with two infinite capacity weighted fair orbit queues, i.e., the re-transmission rate of an orbit depends on the state of the other orbit queue. We consider both exponential and arbitrary distributed service times. In both cases we obtain power series expansions of the generating functions of the stationary joint orbit queue-length distributions, and provide a recursive approach to calculate their coefficients. We also show how to obtain the generating function of the stationary joint orbit queue-length distribution with the aid of a Riemann boundary value problem. Power series approximations are also provided for the model with two independent Poisson streams of jobs with single arrivals. Numerical illustrations are performed and show the accuracy of our approach.

math.PR↗

arXiv2018

A two-class queueing system with constant retrial policy and general class dependent service times

A single server retrial queueing system with two-classes of orbiting customers, and general class dependent service times is considered. If an arriving customer finds the server unavailable, it enters a virtual queue, called the orbit, according to its type. The customers from the orbits retry independently to access the server according to the constant retrial policy. We derive the generating function of the stationary distribution of the number of orbiting customers at service completion epochs in terms of the solution of a Riemann boundary value problem. For the symmetrical system we also derived explicit expressions for the expected delay in an orbit without solving a boundary value problem. A simple numerical example is obtained to illustrate the system's performance.

math.PR↗

arXiv2017

Throughput and Delay Analysis of Wireless Caching Helper Systems with Random Availability

In this paper, we investigate the effect of bursty traffic and random availability of caching helpers in a wireless caching system. More explicitly, we consider a general system consisting of a caching helper with its dedicated user in proximity and another non-dedicated user requesting for content. Both the non-dedicated user and the helper have limited storage capabilities. When the user is not able to locate the requested content in its own cache, then its request shall be served either by the caching helper or by a large data center. Assuming bursty request arrivals at the caching helper from its dedicated destination, its availability to serve other users is affected by the request rate, which will further affect the system throughput and the delay experienced by the non-dedicated user. We characterize the maximum weighted throughput and the average delay per packet of the considered system, taking into account the request arrival rate of the caching helper, the request probability of the user and the availability of the data center. Our results provide fundamental insights in the throughput and delay behavior of such systems, which are essential for further investigation in larger topologies.

cs.IT↗

arXiv2017

Stable Throughput and Delay Analysis of a Random Access Network With Queue-Aware Transmission

In this work we consider a two-user and a three-user slotted ALOHA network with multi-packet reception (MPR) capabilities. The nodes can adapt their transmission probabilities and their transmission parameters based on the status of the other nodes. Each user has external bursty arrivals that are stored in their infinite capacity queues. For the two- and the three-user cases we obtain the stability region of the system. For the two-user case we provide the conditions where the stability region is a convex set. We perform a detailed mathematical analysis in order to study the queueing delay by formulating two boundary value problems (a Dirichlet and a Riemann-Hilbert boundary value problem), the solution of which provides the generating function of the joint stationary probability distribution of the queue size at user nodes. Furthermore, for the two-user symmetric case with MPR we obtain a lower and an upper bound for the average delay without explicitly computing the generating function for the stationary joint queue length distribution. The bounds as it is seen in the numerical results appear to be tight. Explicit expressions for the average delay are obtained for the symmetrical model with capture effect which is a subclass of MPR models. We also provide the optimal transmission probability in closed form expression that minimizes the average delay in the symmetric capture case. Finally, we evaluate numerically the presented theoretical results.

cs.IT↗