Browsing by Subject "Queueing theory"

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
Coordination of staffing and pricing decisions in a service firm
(John Wiley & Sons, 2008) Serel, D. A.; Erel, E.
Customer demand is sensitive to the price paid for the service in many service environments. Using queueing theory framework, we develop profit maximization models for jointly determining the price and the staffing level in a service company. The models include constraints on the average waiting time and the blocking probability. We show convexity of the single-variable subproblem under certain plausible assumptions on the demand and staffing cost functions. Using numerical examples, we investigate the sensitivity of the price and the staffing level to changes in the marginal service cost and the user-specified constraint on the congestion measure.
Open Access
Delay analysis of timer-based frame coalescing in energy efficient ethernet
(IEEE, 2013) Akar, N.
IEEE 802.3az, also known as Energy Efficient Ethernet (EEE), aims at reducing the energy consumption of an Ethernet link by placing it in sleep mode when the link is idle. Frame coalescing mechanism proposed for EEE is an effective means to increase the average idle time of the link, thus reducing the overhead stemming from sleep/wake transitions, but at the expense of increased frame delays. Therefore, it is imperative to quantify the energy-delay trade-off while employing frame coalescing. As opposed to existing delay models that focus only on the average delays, a simple but exact queuing model is introduced for timer-based frame coalescing to find the delay distribution when the frame arrival process is Poisson and frame lengths are generally distributed. An expression for average saving in power consumption is also provided.
Open Access
Dimensioning shared-per-node recirculating fiber delay line buffers in an optical packet switch
(Elsevier, 2013) Akar, N.; Gunalay, Y.
Optical buffering based on fiber delay lines (FDLs) has been proposed as a means for contention resolution in an optical packet switch. In this article, we propose a queuing model for feedback-type shared-per-node recirculating FDL optical buffers in asynchronous optical switching nodes. In this model, optical packets are allowed to recirculate over FDLs as long as the total number of recirculations is less than a pre-determined limit to meet signal loss requirements. Markov Modulated Poisson Process (MMPP)-based overflow traffic models and fixed-point iterations are employed to provide an approximate analysis procedure to obtain blocking probabilities as a function of various buffer parameters in the system when the packet arrival process at the optical switch is Poisson. The proposed algorithm is numerically efficient and accurate especially in a certain regime identified with relatively long and variably-sized FDLs, making it possible to dimension optical buffers in next-generation optical packet switching systems.
Open Access
A general theory on spectral properties of state-homogeneous finite-state quasi-birth-death processes
(Elsevier, 2001) Fadıloğlu, M. M.; Yeralan, S.
In this paper a spectral theory pertaining to Quasi-Birth–Death Processes (QBDs) is presented. The QBD, which is a generalization of the birth–death process, is a powerful tool that can be utilized in modeling many stochastic phenomena. Our theory is based on the application of a matrix polynomial method to obtain the steady-state probabilities in state-homogeneous finite-state QBDs. The method is based on finding the eigenvalue–eigenvector pairs that solve a matrix polynomial equation. Since the computational effort in the solution procedure is independent of the cardinality of the counting set, it has an immediate advantage over other solution procedures. We present and prove different properties relating the quantities that arise in the solution procedure. By also compiling and formalizing the previously known properties, we present a formal unified theory on the spectral properties of QBDs, which furnishes a formal framework to embody much of the previous work. This framework carries the prospect of furthering our understanding of the behavior the modeled systems manifest.
Open Access
An inventory problem with two randomly available suppliers
(Institute for Operations Research and the Management Sciences, 1997) Gürler, Ü.; Parlar, M.
This paper considers a stochastic inventory model in which supply availability is subject to random fluctuations that may arise due to machine breakdowns, strikes, embargoes, etc. It is assumed that the inventory manager deals with two suppliers who may be either individually ON (available) or OFF (unavailable). Each supplier's availability is modeled as a semi-Markov (alternating renewal) process. We assume that the durations of the ON periods for the two suppliers are distributed as Erlang random variables. The OFF periods for each supplier have a general distribution. In analogy with queuing notation, we call this an Es1[Es2]/G1[G2] system. Since the resulting stochastic process is non-Markovian, we employ the "method of stages" to transform the process into a Markovian one, albeit at the cost of enlarging the state space. We identify the regenerative cycles of the inventory level process and use the renewal reward theorem to form the long-run average cost objective function. Finite time transition functions for the semi-Markov process are computed numerically using a direct method of solving a system of integral equations representing these functions. A detailed numerical example is presented for the E2[E2]/M[M] case. Analytic solutions are obtained for the particular case of "large" (asymptotic) order quantity, in which case the objective function assumes a very simple form that can be used to analyze the optimality conditions. The paper concludes with the discussion of an alternative inventory policy for modeling the random supply availability problem.
Open Access
Markov modulated periodic arrival process offered to an ATM multiplexer
(IEEE, 1993-11-12) Akar, Nail; Arıkan, Erdal
When a superposition of on/off sources is offered to a deterministic server, a particular queueing system arises whose analysis has a significant role in ATM based networks. Periodic cell generation during active times is a major feature of these sources. In this paper a new analytical method is provided to solve for this queueing system via an approximation to the transient behavior of the nD/D/1 queue. The solution to the queue length distribution is given in terms of a solution to a linear differential equation with variable coefficients. The technique proposed here has close similarities with the fluid flow approximations and is amenable to extension for more complicated queueing systems with such correlated arrival processes. A numerical example for a packetized voice multiplexer is finally given to demonstrate our results.
Open Access
Markov modulated periodic arrival process offered to an ATM multiplexer
(Elsevier BV * North-Holland, 1995-04) Akar, N.; Arıkan, E.
When a superposition of on/off sources is offered to a deterministic server, we are faced with a particular queueing system, the analysis of which has a significant role in ATM networks. Periodic cell generation during active times is a major feature of these sources. We provide an analytical approach to solve for this queueing system via an approximation to the transient behavior of the nD/D/1 queue. The solution to the queue length distribution is given in terms of a solution to a linear differential equation with variable coefficients. The technique proposed here has close similarities with the fluid flow approximation and is amenable to extension for more complicated queueing systems with such correlated arrival processes. A numerical example for a packetized voice multiplexer is finally given to demonstrate our results.
Open Access
Moments of conditional sojourn times in finite capacity M/M/1/N-PS processor sharing queues
(Institute of Electrical and Electronics Engineers, 2012) Akar, N.
Moments of sojourn times conditioned on the length of an admitted job are derived for a finite capacity M/M/1/N-PS processor sharing queue. The mean conditional sojourn time is given in closed form whereas an expression is provided for the conditional variance in such systems involving matrix-vector operations.
Open Access
A novel queue-aware wireless link adaptation mechanism and its fixed-point analytical model
(SpringerOpen, 2015) Ozturk, O.; Akar, N.
A point-to-point (PTP) wireless link is studied that carries long-lived TCP flows and is controlled with active queue management (AQM). A cross-layer queue-aware adaptive modulation and coding (AMC)-based link adaptation (LA) mechanism is proposed for this wireless link to improve the TCP-level throughput relative to the case where AMC decisions are made based solely on the physical layer (PHY) parameters. The proposed simple-to-implement LA mechanism involves the use of an aggressive modulation and coding scheme (MCS) with high spectral efficiency and high block error rates when the queue occupancy exceeds a certain threshold, but otherwise a relatively conservative MCS with lower spectral efficiency and lower block error rates. A fixed-point analytical model is proposed to obtain the aggregate TCP throughput attained at this wireless link and the model is validated by ns-3 simulations. Numerical experimentation with the proposed analytical model applied to an IEEE 802.16-based wireless link demonstrates the effectiveness of the proposed queue-aware LA (QAWLA) mechanism in a wide variety of scenarios including cases where the channel information is imperfect. The impact of the choice of the queue occupancy threshold of QAWLA is extensively studied with respect to the choice of AQM parameters in order to provide engineering guidelines for the provisioning of the wireless link.
Open Access
Retrial queuing models of multi-wavelength FDL feedback optical buffers
(Institute of Electrical and Electronics Engineers, 2011) Akar, N.; Sohraby, K.
Optical buffers based on Fiber Delay Lines (FDL) have been proposed for contention resolution in optical packet/burst switching systems. In this article, we propose a retrial queuing model for FDL optical buffers in asynchronous optical switching nodes. In the considered system, the reservation model employed is of post-reservation type and optical packets are allowed to re-circulate over the FDLs in a probabilistic manner. We combine the MMPP-based overflow traffic models of the classical circuit switching literature and fixed-point iterations to devise an algorithmic procedure to accurately estimate blocking probabilities as a function of various buffer parameters in the system when packet arrivals are Poisson and packet lengths are exponentially distributed. The proposed algorithm is both accurate and fast, allowing one to use the procedure to dimension optical buffers in next-generation optical packet switching systems.
Open Access
Threshold start-up control policy for polling systems
(Springer, 1998) Günalay, Y.; Gupta, D.
A threshold start-up policy is appealing for manufacturing (service) facilities that incur a cost for keeping the machine (server) on, as well as for each restart of the server from its dormant state. Analysis of single product (customer) systems operating under such a policy, also known as the N-policy, has been available for some time. This article develops mathematical analysis for multiproduct systems operating under a cyclic exhaustive or globally gated service regime and a threshold start-up rule. It pays particular attention to modeling switchover (setup) times. The analysis extends/unifies existing literature on polling models by obtaining as special cases, the continuously roving server and patient server polling models on the one hand, and the standard M/G/1 queue with N-policy, on the other hand. We provide a computationally efficient algorithm for finding aggregate performance measures, such as the mean waiting time for each customer type and the mean unfinished work in system. We show that the search for the optimal threshold level can be restricted to a finite set of possibilities.
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.