Attahiru Sule Alfa

Experimental analysis of simulated annealing based algorithms for the layout problem

Abstract In this paper, results from an experimental analysis involving the 2-way and 3-way exchange algorithms, a modified penalty algorithm, the simulated annealing algorithm and a hybrid simulated annealing algorithm are presented. The hybrid simulated annealing algorithm uses the modified penalty algorithm to generate an initial solution and then improves it using simulated annealing. It is tested on single-row layout problems with facilities of unequal area and multi-row layout problems with facilities of equal area. The algorithm produced solutions better than those previously reported in the literature for two of the larger single-row problems and five multi-row layout problems. For all the other single-row problems and eight of ten multi-row layout test problems, it produced the best known solutions. The hybrid simulated annealing algorithm appears to produce better quality solutions than the simulated annealing and tabu navigation algorithms, but requires more computation time than simulated annealing.

Vacation Models in Discrete Time

A class of single server vacation queues which have single arrivals and non-batch service is considered in discrete time. It is shown that provided the interarrival, service, vacation, and server operational times can be cast with Markov-based representation then this class of vacation model can be studied as a matrix–geometric or a matrix-product problem – both in the matrix–analytic family – thereby allowing us to use well established results from Neuts (1981). Most importantly it is shown that using discrete time approach to study some vacation models is more appropriate and makes the models much more algorithmically tractable. An example is a vacation model in which the server visits the queue for a limited duration. The paper focuses mainly on single arrival and single unit service systems which result in quasi-birth-and-death processes. The results presented in this paper are applicable to all this class of vacation queues provided the interarrival, service, vacation, and operational times can be represented by a finite state Markov chain.

Application of Mobility Prediction in Wireless Networks Using Markov Renewal Theory

An understanding of the network traffic behavior is essential in the evolution of todays wireless networks and thus leads to a more efficient planning and management of the networks scarce bandwidth resources. Prior reservation of radio resources at future locations of a users mobile trajectory can assist in optimizing the allocation of the networks limited resources and sustaining a desirable quality-of-service (QoS) level. This can also help to ensure that the network service can be available anywhere and anytime, which is only possible if, at any time, we can predict from where a user is going to make its demands. In this paper, we apply Markov renewal processes for both mobility modeling and predicting the likelihoods of the next-cell transition, along with anticipating the duration between the transitions, for an arbitrary user in a wireless network. Our proposed prediction technique will also be extended to compute the likelihoods of a user being in a particular state after N transitions. The proposed technique can also be used to estimate the expected spatial-temporal traffic load and activity at each location in a networks coverage area. Using some real traffic data, we illustrate how our proposed prediction method can lead to a significant improvement over some of the conventional methods.

Matrix-geometric solution of discrete time MAP/PH/1 priority queue

We use the matrix-geometric method to study the discrete time MAP/PH/1 priority queue with two types of jobs. Both preemptive and non-preemptive cases are considered. We show that the structure of the R matrix obtained by Miller for the Birth-Death system can be extended to our Quasi-Birth-Death case. For both preemptive and non-preemptive cases the distributions of the number of jobs of each type in the system are obtained and their waiting times are obtained for the non-preemptive. For the preemptive case we obtain the waiting time distribution for the high priority job and the distribution of the lower priority jobs wait before it becomes the leading job of its priority class.

A 3-opt based simulated annealing algorithm for vehicle routing problems

Abstract Simulated Annealing is combined with the 3-opt heuristic to solve the vehicle routing problem. The results are encouraging; two examples out of three large size problems gave results as good as the best known 3-opt solution. Preliminary results with the heuristic algorithm are presented.

ALGORITHMS FOR SOLVING FISK'S STOCHASTIC TRAFFIC ASSIGNMENT MODEL

In this, the logit-based stochastic traffic assignment model is explored. Two new improved algorithms are presented for solving this type of stochastic assignment problem. The major improvement achieved in these algorithms is that the step length in each iteration of the search process is optimized instead of using fixed step lengths as in the existing method of successive averages (MSA).

A PCS network with correlated arrival process and splitted-rating channels

The arrival of calls (i.e., new and handoff calls) in a personal communications services (PCS) network are modeled by a Markov arrival process (MAP) in which we allow correlation of the interarrival times among new calls, among handoff calls, as well as between these two kinds of calls. Each cell of the network consists of a finite number of channels and a buffer with finite size for handoff calls. There exist some channels among each cell which can be used by splitting the original rate into two channels with different rates if necessary when a handoff call arrives and finds all the channels busy. We obtain the stationary joint probability of number of calls in the cell and the phase of the arrival process, the blocking probability of a new call, the forced termination probability of a handoff call, and the mean dwell time of a handoff call in the buffer. Finally, we obtain the distribution and the mean of the cells busy period, the distribution and the mean of the first time to split the cth channel, and some other interesting performance measures for the network. Some explicit results for special cases obtained by Lin et al. (see IEEE Trans. Vech. Technol., vol.45, no.1, p.122-30, 1996 and vol.43, no.3, p.704-12, 1994), Tekinary et al. (1992) and by Yoon et al. (1993) can also be directly obtained from the general conclusion. The results presented can provide guidelines for field data processing in PCS network design and performance evaluation.

Service differentiation in multirate wireless networks with weighted round-robin scheduling and ARQ-based error control

The radio link-level delay statistics in a wireless network using adaptive modulation and coding (AMC), weighted round-robin (WRR) scheduling, and automatic repeat request-based error control is analyzed in this letter. WRR scheduling can be used for service differentiation similar to that achievable by using the generalized processor sharing scheduling discipline. The analytical framework presented in this letter captures physical and radio link-level aspects of a multirate multiuser wireless network (e.g., general fading model, AMC, scheduling, error control) in a unified way. It can be used for admission control and cross-layer design under statistical delay constraints. The analytical results are validated by simulations. Typical numerical results are presented, and their useful implications on the system performance are discussed.

Accurate computation of the smallest eigenvalue of a diagonally dominant M -matrix

If each off-diagonal entry and the sum of each row of a diagonally dominant M-matrix are known to certain relative accuracy, then its smallest eigenvalue and the entries of its inverse are known to the same order relative accuracy independent of any condition numbers. In this paper, we devise algorithms that compute these quantities with relative errors in the magnitude of the machine precision. Rounding error analysis and numerical examples are presented to demonstrate the numerical behaviour of the algorithms.

Performance Analysis of Modified IEEE 802.11-Based Cognitive Radio Networks

This letter considers a modified IEEE 802.11-based cognitive radio network where primary users (PUs) operate on a slot-by-slot basis and secondary users (SUs) try to exploit the time unused by primary users (PUs). To improve the throughput for SUs, our IEEE 802.11-based opportunistic spectrum access (OSA) allows SUs to transmit packets with variable length depending on the remaining time of the current slot. To investigate the throughput for SUs, a novel analytical model is developed. Also, analytical results are validated by extensive simulation.