arXiv subjects

Nail Akar

Publications and source records attributed to Nail Akar.

39 records · Page 3Linked to original sources

arXiv2020

Finding the Exact Distribution of (Peak) Age of Information for Queues of PH/PH/1/1 and M/PH/1/2 Type

Bufferless and single-buffer queueing systems have recently been shown to be effective in coping with escalated Age of Information (AoI) figures arising in single-source status update systems with large buffers and FCFS scheduling. In this paper, for the single-source scenario, we propose a numerical algorithm for obtaining the exact distributions of both the AoI and the peak AoI (PAoI) in (i) the bufferless $PH/PH/1/1/P(p)$ queue with probabilistic preemption with preemption probability $p$, $0 \leq p \leq 1,$ and (ii) the single buffer $M/PH/1/2/R(r)$ queue with probabilistic replacement of the packet in the queue by the new arrival with replacement probability $r$, $0 \leq r \leq 1$. The proposed exact models are based on the well-established theory of Markov Fluid Queues (MFQ) and the numerical algorithms are matrix-analytical and they rely on numerically stable and efficient vector-matrix operations. Moreover, the obtained exact distributions are in matrix exponential form, making it amenable to calculate the tail probabilities and the associated moments straightforwardly. Firstly, we validate the accuracy of the proposed method with simulations, and for sume sub-cases, with existing closed-form results. We then comparatively study the AoI performance of the queueing systems of interest under varying traffic parameters.

cs.IT↗

arXiv2019

The MAP/M/s+G Call Center Model with General Patience Times: Stationary Solutions and First Passage Times

We study the MAP/M/s+G queuing model with MAP (Markovian Arrival Process) arrivals, exponentially distributed service times, infinite waiting room, and generally distributed patience times. Using sample-path arguments, we propose to obtain the steady-state distribution of the virtual waiting time and subsequently the other relevant performance metrics of interest for the MAP/M/s+G queue by means of finding the steady-state solution of a properly constructed Continuous Feedback Fluid Queue (CFFQ). The proposed method is exact when the patience time is a discrete random variable and is asymptotically exact when it is continuous/hybrid for which case discretization of the patience time distribution and subsequently the steady-state solution of a Multi-Regime Markov Fluid Queue (MRMFQ) is required. Besides the steady-state distribution, we also propose a new method to approximately obtain the first passage time distribution for the virtual and actual waiting times in the $MAP/M/s+G$ queue. Again, using sample-path arguments, finding the desired distribution is also shown to reduce to obtaining the steady-state solution of a larger dimensionality CFFQ where the deterministic time horizon is to be approximated by Erlang or Concentrated Matrix Exponential (CME) distributions. Numerical results are presented to validate the effectiveness of the proposed method.

cs.PF↗

arXiv2017

Joint Cell Muting and User Scheduling in Multi-Cell Networks with Temporal Fairness

A semi-centralized joint cell muting and user scheduling scheme for interference coordination in a multicell network is proposed under two different temporal fairness criteria. The main principle behind the proposed scheme is that a central entity selects a cell muting pattern out of a pattern set at a decision instant, and subsequently the un-muted base stations opportunistically schedule the users in the associated cells, both decisions made on a temporal-fair basis. Although some pattern sets are easily obtainable from static frequency reuse systems, we propose a more general pattern set construction algorithm in this paper. As for the first fairness criterion, all cells are assigned to receive the same temporal share with the ratio between the temporal share of a cell center section and that of the cell edge section is set to a fixed desired value for all cells. The second fairness criterion is based on the max-min temporal fairness for which the temporal share of the network-wide worst-case user is maximized. Numerical results are provided to validate the effectiveness of the proposed scheme for both criteria. The impact of choice of the cell muting pattern set is also studied through numerical examples for various cellular topologies.

cs.NI↗