Browsing by Subject "Queuing theory."

Now showing 1 - 9 of 9

Open Access
Analytical modeling of multi-channel optical burst switching with multiple traffic classes
(2011) Dinç, Volkan
In this thesis, we study an Optical Burst Switching (OBS) node with links carrying multiple wavelength channels (called hereafter channels) with multiple traffic classes. We assume that offset-based service differentiation is used to differentiate among these traffic classes in terms of packet loss probabilities. We first propose a basic scheme, called bLAUC (Basic Latest Available Unused Channel) for channel scheduling. Although practicality of the bLAUC scheme is relatively limited when compared to other conventional schedulers such as LAUC, we study bLAUC in this thesis due to its tractability to analysis and moreover bLAUC possesses certain crucial properties of conventional schedulers. We then propose an iterative procedure to approximate per-class loss probabilities for the OBS link of interest when packet arrivals to the link are Poisson and packet lengths are exponentially distributed. In our iterative procedure, we model a multi-channel OBS link with Poisson arrivals by a single channel Markov fluid queue with occupancy-dependent packet arrival intensities. The proposed procedure provides acceptable approximations for a wide range of scenarios with relatively low complexity. Consequently, the proposed procedure can be used in optimization problems concerning multiclass OBS and in finding guidelines to effectively utilize OBS resources under loss probability constraints.
Open Access
Asymptotic analysis of highly reliable retrial queueing systems
(2000) Kurtuluş, Mümin
The thesis is concerned with the asymptotic analysis of the time of first loss of a customer and the flow of lost customers in some types of Markov retrial queueing systems with flnite buffer. A retrial queueing system is characterized by the following feature: an arriving customer finding all of the servers busy must leave the service area and join a special buffer. After this it may re-apply for service after some random time. If the buffer is full the customer is lost. The analysis of the time of first loss of a customer is based on the method of so-called S — sets and the results about the asymptotic behavior of the first exit time from the fixed subset of states of semi-Markov process of a special structure (so-called monotone structure). Single server retrial queueing systems [M IM IlIm with retrials) as well as multiple server retrial queueing systems {M IM fsfm with retrials) are analyzed in cases of fast service and both fast service and fast retrials. Exponential approximation for the time of first loss and Poisson approximation for the flow of lost customers are proved for all of the considered cases.
Open Access
Characterization of envy free solutions for queuing problems
(2006) Esmerok, İbrahim Barış
In this study we are working on queuing problems. In our model a solution to a queuing problem is an ordering of agents and a transfer vector where the sum of the transfers of agents is equal to zero. Hence a queuing problem is a double, where we have a finite set of agents and a profile of payoff functions of agents which represent their preferences on their orderings and transfers. We are assuming that the payoff functions of agents are quasi-linear on transfers. Our main aim is to find envy free solutions for queuing problems. Since payoff functions of agents are quasi-linear envy freeness implies Pareto efficiency. For problems where there are less than five agents, we show that the set of envy free solutions is not empty and we are able to characterize the envy free solutions. We conjecture that our results may be extended to general case similar to our extension from three person case to four person case. When we assume that a queuing problem satisfies order preservation property we are able to characterize envy free solutions with a solution concept that we introduce in this study.
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
Kronecker-based infinite level-dependent QBDS : matrix analytic solution versus simulation
(2011) Orhan, Muhsin Can
Markovian systems with multiple interacting subsystems under the influence of a control unit are considered. The state spaces of the subsystems are countably in- finite, whereas that of the control unit is finite. A recent infinite level-dependent quasi-birth-and-death (LDQBD) model for such systems is extended by facilitating the automatic representation and generation of the nonzero blocks in its underlying infinitesimal generator matrix with sums of Kronecker products. Experiments are performed on systems of stochastic chemical kinetics having two or more countably infinite state space subsystems. Results indicate that, albeit more memory consuming, there are many cases where a matrix analytic solution coupled with Lyapunov theory yields a faster and more accurate steady-state measure compared to that obtained with simulation.
Open Access
M/M/1 polling models with two finite queues
(1995) Daşçı, Abdullah
Polling models are special kinds of queueing models where multiple-customer type single-stage is considered. In this thesis, first an overview and a classification of polling models will be given. Then two-costomer one server M /M /l polling models will be analyzed and the performance of models will be developed for exhaustive, gated, and G-limited service policies. We give analytical methods for a special type of polling model where we solve the system to get mean queue lengths and thruput rates by three methods. The first one is based on solving the steady state distribution of the Markov Process. The second is a decompositon aiming to decrease the size of the problem. The third one is an approximation method that uses the earlier results and it is very accurate. The thesis will be concluded with possible future extensions.
Open Access
Performance analysis of generic discrete-time queues and applications to telecommunication networks
(2001) Kavak, Egemen Değer
Open Access
Performance evaluation of telecommunication networks based on multi-regime fluid queues
(2009) Kankaya, Hüseyin Emre
Today’s state-of-the-art search engines utilize the inverted index data structure for fast text retrieval on large document collections. To parallelize the retrieval process, the inverted index should be distributed among multiple index servers. Generally the distribution of the inverted index is done in either a term-based or a document-based fashion. The performances of both schemes depend on the total number of disk accesses and the total volume of communication in the system. The classical approach for both distributions is to use the Central Broker Query Evaluation Scheme (CB) for parallel text retrieval. It is known that in this approach the central broker is heavily loaded and becomes a bottleneck. Recently, an alternative query evaluation technique, named Pipelined Query Evaluation Scheme (PPL), has been proposed to alleviate this problem by performing the merge operation on the index servers. In this study, we analyze the scalability and relative performances of the CB and PPL under various query loads to report the benefits and drawbacks of each method.
Open Access
Weighted round robin scheduling in input-queued packet switches subject to deadline constraints
(2000) Rai, Idris A.
In this thesis work, the problem of scheduling deadline constrained traffic is studied. The problem is explored in terms of Weighted Round Robin (WRR) service discipline in input queued packet switches. Application of the problem may arise in packet switching networks and Satellite-Switched Time Division Multiple Access (SS/TDMA) systems. A new formulation of the problem is presented. The main contribution of the thesis is a ’’backward extraction” technique to schedule packet forwarding through the switch fabric. A number of heuristic algorithms, each based on backward extraction, are proposed, and their performances are studied via simulation. Numerical results show that the algorithms perform significantly better than earlier proposed algorithms. The experimental results strongly assert Philp and Liu conjecture.