ABDELGHANI BEN TAHAR - Academia.edu (original) (raw)

Papers by ABDELGHANI BEN TAHAR

Mathematical Methods of Operations Research, Nov 1, 2002

Dupuis and Williams proved that a su‰cient condition for the positive recurrence for a semimartin... more Dupuis and Williams proved that a su‰cient condition for the positive recurrence for a semimartingale reflecting Brownian motion in an orthant (SRBM) with data ðy; R; S; DÞ, is that the corresponding Linear Skorohod Problem LSPðyÞ is stable. In this paper we use the linear complementary problem to give necessary conditions, on y A R n and matrix R, under which the linear Skorohod problem LSPðyÞ is stable. In the three dimensional case we characterize the vectors y A R 3 such that the LSPðyÞ is stable.

A critical issue in modern server farm system architecture is to know how to efficiently allocate... more A critical issue in modern server farm system architecture is to know how to efficiently allocate the number of servers to manage unpredictable demand patterns, in order to get the best performance without wasting energy. Although it is demanded to shut down servers when they become inactive to save energy, the high configuration cost (in terms of setup time and energy consumption) required to restart the server can affect performance. The problem is even more complicated since today's servers offer several states of sleep or standby that allow the setup cost to be balanced by the power consumed while the server is "in sleep". In this paper, we will consider the M/M/k queuing system with setup costs: M/M/k/Setup. Servers are obviously shut down when there is no work to be done, but turning on a server that has been shut down will incur setup costs. The setup cost takes the shape of a delay and a power penalty, event that idle servers are shut down to save on running expenses. Since servers in setup mode consume a lot of energy, the number of servers that can be in setup at any given time is often limited. In the configuration model, a maximum of one server can be setup at any time. The proposed mechanism and its performance parameters are described by a a mathematical model. In addition, the effect of the proposed mechanism on energy consumption behaviour is assessed. The discussion on the results shows the role of the consideration of reserves in the system.

Consider a single server queueing system with several classes of customers, each having its own r... more Consider a single server queueing system with several classes of customers, each having its own renewal input process and its own general service times distribution. Upon completing service, customers may leave, or reenter the queue, possibly as customers of a different class. The server is operating under the egalitarian or the discriminatory processor sharing discipline. In this paper, we consider the fluid approximation of this multiclass processor sharing queue. We first provide the results allowing to compute the trajectories for this model, under the egalitarian PS discipline. Asymptotic results for overloaded queues are also stated. Next, we show that a simple transformation allows to compute the solution for the discriminatory PS queue as well. Finally, we illustrate the different results through numerical experiments. We compare transient trajectories with simulations, and we discuss the fairness issue that may arise in overloaded PS queues.

Queueing Systems, Feb 23, 2012

In this paper we consider the variational problem in the non-negative orthant of R 3. The solutio... more In this paper we consider the variational problem in the non-negative orthant of R 3. The solution of this problem gives the large deviation rate function for the stationary distribution of an SRBM (Semimartingal Reflecting Brownian Motion). Avram, Dai and Hasenbein (Queueing Syst. 37, 259-289, 2001) provided an explicit solution of this problem in the non-negative quadrant. Building on this work, we characterize reflective faces of the non-negative orthant of R d , we construct boundary influence cones and we provide an explicit solution of several constrained variational problems in R 3. Moreover, we give conditions under which certain spiraling paths to a point on an axis have a cost which is strictly less than the cost of every direct path and path with two pieces.

Stochastics and Stochastics Reports, 2000

ABSTRACT

Due to the complex and dynamic nature of virtual machine allocation in the cloud, it is difficult... more Due to the complex and dynamic nature of virtual machine allocation in the cloud, it is difficult to manage and control the resources or to choose the best allocation of these resources. In this paper, we propose an optimal model for allocating computing resources to assess the best management of system resources where a group of physical machines is defined as ”reserves”. The controller activates them one by one when the system has a high number of tasks. The objective is to maximize the reward of the cloud computing system. This reward is calculated based on the energy and execution time of each customer and the characteristics of the system. Finding the best allocation for such a complex system is a challenge. For this, we used a heuristic algorithm and dynamic programming approach. The results analysis showed the advantage of using our model to control the use of reserve machines to get high quality of service and low energy consumption.

Mathematical Modelling of Engineering Problems, 2021

In intelligent transportation systems, Vehicular Cloud Computing (VCC) is a new technology that c... more In intelligent transportation systems, Vehicular Cloud Computing (VCC) is a new technology that can help ensure road security and transport efficiency. The study and evaluation of performances of a VCC is a topic of crucial interest in these environments. This paper presents a model of the computation resource allocation problem in VCC by considering heterogeneity and priority of service requests. We consider service requests from two classes, Primary service requests and Secondary service requests. We involve a Semi-Markov Decision Process (SMDP) to achieve the optimal policy that maximizes the performances of the VCC system taking into account the variability of resources, the income and the system cost. We utilize an iterative approach to achieve the optimal scheme that characterizes the action to be taken under each state. We validate our study by numerical results that show the effectiveness of the proposed SMDP-based scheme.

A sequence of finite tandem queue is considered for this study. Each one has a single server, whi... more A sequence of finite tandem queue is considered for this study. Each one has a single server, which operates under the egalitarian processor sharing discipline. External customers arrive at each queue according to a renewal input process and having a general service times distribution. Upon completing service, customers leave the current queue and enter to the next. Under mild assumptions, including critical data, we prove the existence and the uniqueness of the fluid solution. For asymptotic behavior, we provide necessary and sufficient conditions for the invariant state and the convergence to this invariant state. In the end, we establish the convergence of a correctly normalized state process to a fluid limit characterized by a system of algebraic and integral equations. Keywords—Fluid Limit, fluid model, measure valued process, processor sharing, tandem queue.

Advances in Intelligent Systems and Computing, 2018

In the context of cloud computing, the energy consumed by the data center is higher because it co... more In the context of cloud computing, the energy consumed by the data center is higher because it contains a large number of physical machines, which in turn contain a number of virtual machines resulting in high power consumption. In addition, the cloud provider must provide a high quality of service (QoS) to its customers on the condition of not consuming a large amount of energy. Among the techniques of minimizing energy consumption is to turn down servers when the workload is low and relocate its virtual machines to another server. In this paper, we propose to combine this technique with another that uses a threshold ensuring the condition of not crossing a given level of use capacity of each server. We validate our model by numerical evaluation which demonstrates the effectiveness of the proposition in terms of energy efficiency and QoS improvement.

International Journal of Engineering & Technology, 2018

As a result of the dynamic nature of Virtual Machine allocation in cloud computing, it is not eas... more As a result of the dynamic nature of Virtual Machine allocation in cloud computing, it is not easy to manage system resources or choose the best configuration based solely on human experience. In this work, we used stochastic modelling instead of comprehensive experiments to evaluate the best resource management of the system. In such complex systems, choosing the best decision is a challenge, for this reason we have designed a heuristic algorithm, specifically, dynamic programming as a resource management and programming tool that finds a way that attempts to satisfy the conflicting objectives of high performance and low power consumption. As a scenario for using this algorithm, we addressed the problem of virtual machine allocation, a subset of physical machines is designated as "reserve", and the reserves are actives when the number of jobs in the system is sufficiently high. The question is how to decide when to activate the reserves. The simulation results demonstrat...

Queueing Systems, 2012

Proceedings of the 4th International ICST Conference on Performance Evaluation Methodologies and Tools, 2009

Mathematical Methods of Operations Research (ZOR), 2002