Browsing by Subject "Markov fluid queues"

Now showing 1 - 13 of 13

Open Access
Analysis of continuous feedback Markov fluid queues and its applications to modeling Optical Burst Switching
(IEEE, 2013) Yazıcı, Mehmet Akif; Akar, Nail
Optical Burst Switching (OBS) has been proposed as a candidate technology for the next-generation Internet. In OBS, packets are assembled into a burst, and a burst control packet is sent in advance to inform and reserve resources at the optical nodes in the path of the burst. In this study, we analyze the horizon-based reservation scheme in OBS using Markov fluid queues. First, we provide a solution to continuous feedback Markov fluid queues, then we model the horizon-based reservation scheme as a continuous feedback Markov fluid queue and numerically study it. We provide numerical examples to validate our model and its solution technique as well as to obtain some insight on the horizon-based reservation mechanism. © 2013 IEEE.
Open Access
Exact analysis of offset-based service differentiation in single-channel multi-class OBS
(IEEE, 2009) Kankaya, H. E.; Akar, N.
We study a multi-class optical burst switching (OBS) node using the horizon reservation scheme. Multiple traffic classes are differentiated using different offset times per class. Assuming Poisson burst arrivals and phase-type distributed burst lengths, we exactly solve for per-class blocking probabilities using the well-known theory of feedback Markov fluid queues.
Open Access
Exact distribution of age of information (AoI) and peak AoI in single-source and multi-source status update systems
(2021-07) Doğan, Ozancan
In this thesis, we ﬁrst study buﬀerless and single-buﬀer single-source queueing models of a status update system with various accompanying buﬀer manage-ment schemes. Next, we study the buﬀerless multi-source queueing model of a status-update system with probabilistic preemption. For both single-source and multi-source queueing models, we obtain the exact distributions of the associ-ated Age of Information (AoI) and Peak Age of Information (PAoI) processes. For this purpose, we propose a Markov Fluid Queue (MFQ) model for both scenarios out of which the exact AoI distributions are derived. The numerical so-lution obtained from the proposed model provides the distributional expressions in matrix-exponential form out of which one can easily obtain their high order moments. We validate the accuracy of our proposed algorithm by comparing our results with simulations and also existing results in the literature in certain sub-cases. Numerical results are presented to provide engineering insight on how state update systems need to be conﬁgured and operated.
Open Access
Feedback fluid queues with multiple tresholds
(2006) Kankaya, Hüseyin Emre
Unlike discrete or continuous time queuing systems fed with point processes, workload in fluid queues arrives at the system as a fluid flow rather than jobs or packets. The rate of the fluid flow is governed by a continuous time Markov chain in Markov fluid queues. In first order fluid queues, rates are deterministically determined by a background Markov chain whereas in second order fluid queues, a Brownian motion is additionally inserted to the queue content process. Each of those queues can either accommodate a single regime or multiple regimes (equivalently multiple thresholds) in which the rates and the infinitesimal generator might be different in different regimes but they should be fixed within a single regime. In this thesis, we first generalize the existing solution of first order feedback fluid queues with multiple thresholds for the steady state distribution function of queue occupancy by also allowing the existence of repulsive type boundaries and states with zero rates. Secondly, we complete the boundary conditions for not only the transient but also the steady state solution of second order feedback fluid queues with multiple thresholds. Finally, we apply the theory of feedback fluid queues with multiple thresholds as an effective approximation to the Markov modulated discrete time queueing model that arises in the performance evaluation of an adaptive MPEG video streaming system in UMTS environment. By doing so, we eliminate the state space explosion problem that arises in the original discrete model.
Open Access
Finding the exact distribution of (peak) age of information for queues of PH/PH/1/1 and M/PH/1/2 type
(IEEE, 2020) Akar, Nail; Doğan, Ozancan; Atay, Eray Ünsal
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 ≤ p ≤ 1, and (ii) the single buffer M/P H/1/2/R(r) queue with probabilistic replacement of the packet in the queue by the new arrival with replacement probability r, 0 ≤ r ≤ 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.
Open Access
The finite/infinite horizon ruin problem with multi-threshold premiums: a Markov fluid queue approach
(Springer New York LLC, 2017) Yazici, M. A.; Akar, N.
We present a new numerical method to obtain the finite- and infinite-horizon ruin probabilities for a general continuous-time risk problem. We assume the claim arrivals are modeled by the versatile Markovian arrival process, the claim sizes are PH-distributed, and the premium rate is allowed to depend on the instantaneous risk reserve in a piecewise-constant manner driven by a number of thresholds, i.e., multi-threshold premiums. We introduce a novel sample path technique by which the ruin problems are shown to reduce to the steady-state solution of a certain multi-regime Markov fluid queue. We propose to use the already existing numerically efficient and stable numerical algorithms for such Markov fluid queues. Numerical results are presented to validate the effectiveness of the proposed method regarding the computation of the finite- and infinite-horizon ruin probabilities for risk models including those with relatively large number of thresholds.
Open Access
Markov fluid queue model of an energy harvesting IoT device with adaptive sensing
(Elsevier B.V., 2017) Tunc C.; Akar, N.
Energy management is key in prolonging the lifetime of an energy harvesting Internet of Things (IoT) device with rechargeable batteries. Such an IoT device is required to fulfill its main functionalities, i.e., information sensing and dissemination at an acceptable rate, while keeping the probability that the node first becomes non-operational, i.e., the battery level hits zero the first time within a given finite time horizon, below a desired level. Assuming a finite-state Continuous-Time Markov Chain (CTMC) model for the Energy Harvesting Process (EHP), we propose a risk-theoretic Markov fluid queue model for the computation of first battery outage probabilities in a given finite time horizon. The proposed model enables the performance evaluation of a wide spectrum of energy management policies including those with sensing rates depending on the instantaneous battery level and/or the state of the energy harvesting process. Moreover, an engineering methodology is proposed by which optimal threshold-based adaptive sensing policies are obtained that maximize the information sensing rate of the IoT device while meeting a Quality of Service (QoS) constraint given in terms of first battery outage probabilities. Numerical results are presented for the validation of the analytical model and also the proposed engineering methodology, using a two-state CTMC-based EHP.
Open Access
The multi-source probabilistically preemptive M/PH/1/1 queue with packet errors
(IEEE, 2021-08-20) Doğan, Ozancan; Akar, Nail
Analytical modeling of Age of Information (AoI) and Peak AoI (PAoI) has recently drawn a lot of attention in the context of quantitative assessment of information freshness in status update systems. In this paper, we study a probabilistically preemptive bufferless M/PH/1/1 queue fed with information update packets from N separate information sources for which a new information packet arrival from source- m is allowed to preempt a packet from source- n in service, with a probability depending on n and m . To make the model even more general than the existing ones, we assume a distinct phase-type (PH-type) service time distribution, a distinct packet error and retransmission probability, for each of the information sources. Using sample path arguments and the theory of Markov Fluid Queues (MFQ), the exact distributions of the AoI and PAoI are numerically obtained for each of the sources. Numerical examples are provided to demonstrate the impact of various system parameters on AoI performance. In the context of a two-source system, we present a methodology on how to optimally choose the preemption probabilities and packet generation rates so as to minimize certain AoI-oriented cost functions.
Open Access
On the Queuing Model of the energy-delay tradeoff in wireless links with power control and link adaptation
(IEEE, 2019-05) Gamgam, Ege Orkun; Tunç, Çağlar; Akar, Nail
A transmission profile refers to a transmission power and a modulation and coding scheme to be used for packet transmissions over a wireless link. The goal of this paper is to develop transmission profile selection policies so as to minimize the average power consumption on a wireless link while satisfying a certain delay constraint given in terms of a delay violation probability. Toward the assessment of profile selection policies, a multi-regime Markov fluid queue model is proposed to obtain the average power consumption and the queue waiting time distribution which allows one to analyze the energy-delay tradeoff in queuing systems for which the packet transmission duration is allowed to depend on the delay experienced by the packet until the beginning of service. Numerical examples are presented with transmission profiles obtained from realistic LTE simulations. Several transmission profile selection policies are proposed and subsequently compared using the analytical model.
Open Access
Performance modeling of QoS differentiation in optical packet switching via FDL access limitation
(Springer New York LLC, 2017) Yazici, M. A.; Akar, N.
We present an exact analytical model for single-wavelength quality of service (QoS) differentiation in a two-class optical packet switch. In this system, QoS differentiation is achieved by limiting the set of fiber delay lines (FDLs) to the low-priority class, whereas the high-priority class is allowed to access the entire FDL bank. The analytical model is based on multi-regime Markov fluid queues and is extensible to multi-class systems with more than two classes. Markovian arrival process packet arrivals and phase-type distributed packet sizes are considered for the purpose of generality. The proposed analytical model is validated through simulations. The numerical results provide insight into determining appropriate subsets of FDLs allowed for the access of the low-priority class. The results also show that it is possible to direct almost all the packet losses to the low-priority class under moderate loads.
Open Access
Solving multi-regime feedback fluid queues
(Taylor & Francis Inc., 2008) Kankaya, H. E.; Akar, N.
In this paper, we study Markov fluid queues with multiple thresholds, or the so-called multi-regime feedback fluid queues. The boundary conditions are derived in terms of joint densities and for a relatively wide range of state types including repulsive and zero drift states. The ordered Schur factorization is used as a numerical engine to find the steady-state distribution of the system. The proposed method is numerically stable and accurate solution for problems with two regimes and 210 states is possible using this approach. We present numerical examples to justify the stability and validate the effectiveness of the proposed approach.
Open Access
Steady-state and first passage time distributions for waiting times in the MAP/M/s+G queueing model with generally distributed patience times
(AIMS Press, 2022-11-30) Gürsoy, Ömer; Mehr, Kamal Adli; Akar, Nail
We study the MAP/M/s+G queueing model that arises in various multi-server engineering problems including telephone call centers, under the assumption of 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 via the steady-state solution of a certain 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 is required giving rise to a computational complexity depending linearly on the number of discretization levels. Additionally, a novel method is proposed to accurately obtain the first passage time distributions for the virtual and actual waiting times again using CFFQs while approximating the deterministic time horizons by Erlang distributions or more efficient Concentrated Matrix Exponential (CME) distributions. Numerical results are presented to validate the effectiveness of the proposed numerical method.
Open Access
The workload-dependent MAP/PH/1 queue with infinite/finite workload capacity
(Elsevier, 2013) Yazici, M. A.; Akar, N.
We propose a numerical algorithm for finding the steady-state queue occupancy distribution for a workload-dependent MAP/PH/1 queue in which the arrival process and the service rate depend continuously on the instantaneous workload in the system. Both infinite and finite queue capacity scenarios are considered, including partial rejection and complete rejection policies for the latter. Using discretization, this system is approximately described by a multi-regime Markov fluid queue for which numerical algorithms are available. The computational complexity of the proposed method is linear in the number of regimes used for discretization. We provide numerical examples to validate the proposed approach.