Browsing by Subject "Poisson distribution"

Now showing 1 - 10 of 10

Open Access
Analytical performance modeling of elastic optical links with aligned spectrum allocation
(Elsevier BV North-Holland, 2015) Vaezi, K.; Akar, N.
Abstract Elastic optical networking has recently been proposed for use in optical transport networks to cope with increasingly heterogeneous and dynamic demand patterns. In this paper, we study the blocking performance of a multi-class elastic optical link for which a demand needs to be allocated a contiguous subset of the entire spectrum. This problem is different than the well-known blocking problem in multi-class multi-server loss systems due to the contiguous allocation constraint. We first propose a non-work-conserving aligned spectrum allocation policy which is shown to outperform the conventional first fit-based work-conserving allocation policy without alignment. Subsequently, for blocking performance of an aligned elastic optical link with up to three different traffic classes, we propose a novel and systematic order reduction procedure for MMPPs (Markov Modulated Poisson Process) and use this procedure as the numerical engine to approximately obtain the blocking probabilities. The proposed numerical algorithm is validated under various system and traffic parameters and is shown to be effectively usable as an instrument to dimension elastic optical links.
Open Access
Capacity bounds for the poisson-repeat channel
(Institute of Electrical and Electronics Engineers, 2023-08-22) Kazemi, Mohammad; Duman, Tolga M.
We develop bounds on the capacity of Poisson-repeat channels (PRCs) for which each input bit is independently repeated according to a Poisson distribution. The upper bounds are obtained by considering an auxiliary channel where the output lengths corresponding to input blocks of a given length are provided as side information at the receiver. Numerical results show that the resulting upper bounds are significantly tighter than the best known one for a large range of the PRC parameter ? (specifically, for ? =0.35). We also describe a way of obtaining capacity lower bounds using information rates of the auxiliary channel and the entropy rate of the provided side information.
Open Access
Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering
(Elsevier, 2005) Pekergin, N.; Dayar T.; Alparslan, D. N.
This paper presents an improved version of a componentwise bounding algorithm for the state probability vector of nearly completely decomposable Markov chains, and on an application it provides the first numerical results with the type of algorithm discussed. The given two-level algorithm uses aggregation and stochastic comparison with the strong stochastic (st) order. In order to improve accuracy, it employs reordering of states and a better componentwise probability bounding algorithm given st upper- and lower-bounding probability vectors. Results in sparse storage show that there are cases in which the given algorithm proves to be useful. © 2004 Elsevier B.V. All rights reserved.
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
The impact of price skimming on supply and exit decisions
(John Wiley & Sons, 2015) Toptal, A.; Çetinkaya, S.
Stochastic inventory control theory has focused on the order and/or pricing policy when the length of the selling period is known. In contrast to this focus, we examine the optimal length of the selling period - which we refer to as market exit time - in the context of a novel inventory replenishment problem faced by a supplier of a new, trendy, and relatively expensive product with a short life cycle. An important characteristic of the problem is that the supplier applies a price skimming strategy over time and the demand is modeled as a nonhomogeneous Poisson process with an intensity that is dependent on time. The supplier's problems of finding the optimal order quantity and market exit time, with the objective of maximizing expected profit, is studied. Procedures are proposed for joint optimization of the objective function with respect to the order quantity and the market exit time. Then, the effects of the order quantity and market exit time on the supplier's profitability are explored on the basis of a quantitative investigation.
Open Access
Optimal control of a two-stage stochastic hybrid manufacturing system with Poisson arrivals and exponential service times
(IEEE, 2005) Gökbayrak, Kağan; Selvi, Ömer
Extending earli'er work on single-stage stochastic hybrid system models, we consider a two-stage stochastic hybrid system where the job arrivals are represented through a Poisson process, and the service times required to attain a desired physical state are exponentially distributed dependent on the controllable process rates. For the case where the costs associated with the process rates and the inventory levels are non-decreasing convex, and the process rates take values from finite sets, we show that there exist threshold policies on both inventory levels for selecting the optimal process rates at each station.
Open Access
Performance analysis of an optical packet switch employing full/limited range share per node wavelength conversion
(IEEE, 2007) Akar, Nail; Karasan, Ezhan; Muretto, G.; Raffaelli, C.
In this paper, we study an asynchronous optical packet switching node equipped with a number of limited range or full range wavelength converters shared per node. The packet traffic is realistically modeled by a superposition of a finite number of on-off sources as opposed to the traditional Poisson model which ignores the limited number of ports on a switch. We both study circular and non-circular limited range wavelength conversion schemes. In our simulations, we employ the far conversion policy where the optical packet is switched onto the farthest available wavelength in the tuning range, which is known to outperform the random conversion policy. We propose an approximate analytical method based on block tridiagonal Markov chains and fixed point iterations to solve for the blocking probabilities in share per node wavelength conversion systems. The method provides an accurate approximation for full range systems and acceptable results for limited range systems.
Open Access
Quality control chart design under jidoka
(John Wiley & Sons, Inc., 2009) Berk, E.; Toy, A. Ö.
We consider design of control charts in the presence of machine stoppages that are exogenously imposed (as under jidoka practices). Each stoppage creates an opportunity for inspection/repair at reduced cost. We first model a single machine facing opportunities arriving according to a Poisson process, develop the expressions for its operating characteristics and construct the optimization problem for economic design of a control chart. We, then, consider the multiple machine setting where individual machine stoppages may create inspection/repair opportunities for other machines. We develop exact expressions for the cases when all machines are either opportunity-takers or not. On the basis of an approximation for the all-taker case, we then propose an approximate model for the mixed case. In a numerical study, we examine the opportunity taking behavior of machines in both single and multiple machine settings and the impact of such practices on the design of an X̄ - Q C chart. Our findings indicate that incorporating inspection/repair opportunities into QC chart design may provide considerable cost savings.
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
State-dependent control of a single stage hybrid system with poisson arrivals
(2011) Gokbayrak, K.
We consider a single-stage hybrid manufacturing system where jobs arrive according to a Poisson process. These jobs undergo a deterministic process which is controllable. We define a stochastic hybrid optimal control problem and decompose it hierarchically to a lower-level and a higher-level problem. The lower-level problem is a deterministic optimal control problem solved by means of calculus of variations. We concentrate on the stochastic discrete-event control problem at the higher level, where the objective is to determine the service times of jobs. Employing a cost structure composed of process costs that are decreasing and strictly convex in service times, and system-time costs that are linear in system times, we show that receding horizon controllers are state-dependent controllers, where state is defined as the system size. In order to improve upon receding horizon controllers, we search for better state-dependent control policies and present two methods to obtain them. These stochastic-approximation-type methods utilize gradient estimators based on Infinitesimal Perturbation Analysis or Imbedded Markov Chain techniques. A numerical example demonstrates the performance improvements due to the proposed methods. © 2011 Springer Science+Business Media, LLC.