Price Faculty of Engineering Scholarly Works
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Browsing Price Faculty of Engineering Scholarly Works by Author "Alfa, Attahiru S"
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- ItemOpen AccessA discrete single server queue with Markovian arrivals and phase type group services(1995-1-1) Alfa, Attahiru Sule; Dolhun, K. Laurie; Chakravarthy, S.We consider a single-server discrete queueing system in which arrivals occur according to a Markovian arrival process. Service is provided in groups of size no more than M customers. The service times are assumed to follow a discrete phase type distribution, whose representation may depend on the group size. Under a probabilistic service rule, which depends on the number of customers waiting in the queue, this system is studied as a Markov process. This type of queueing system is encountered in the operations of an automatic storage retrieval system. The steady-state probability vector is shown to be of (modified) matrix-geometric type. Efficient algorithmic procedures for the computation of the rate matrix, steady-state probability vector, and some important system performance measures are developed. The steady-state waiting time distribution is derived explicitly. Some numerical examples are presented.
- ItemOpen AccessA finite capacity queue with Markovian arrivals and two servers with group services(1994-1-1) Chakravarthy, S.; Alfa, Attahiru SuleIn this paper we consider a finite capacity queuing system in which arrivals are governed by a Markovian arrival process. The system is attended by two exponential servers, who offer services in groups of varying sizes. The service rates may depend on the number of customers in service. Using Markov theory, we study this finite capacity queuing model in detail by obtaining numerically stable expressions for (a) the steady-state queue length densities at arrivals and at arbitrary time points; (b) the Laplace-Stieltjes transform of the stationary waiting time distribution of an admitted customer at points of arrivals. The stationary waiting time distribution is shown to be of phase type when the interarrival times are of phase type. Efficient algorithmic procedures for computing the steady-state queue length densities and other system performance measures are discussed. A conjecture on the nature of the mean waiting time is proposed. Some illustrative numerical examples are presented.
- ItemOpen AccessComputational Procedures for a Class of GI/D/k Systems in Discrete Time(2009-11-5) Rahman, Md. Mostafizur; Alfa, Attahiru SuleA class of discrete time GI/D/ systems is considered for which the interarrival times have finite support and customers are served in first-in first-out (FIFO) order. The system is formulated as a single server queue with new general independent interarrival times and constant service duration by assuming cyclic assignment of customers to the identical servers. Then the queue length is set up as a quasi-birth-death (QBD) type Markov chain. It is shown that this transformed GI/D/1 system has special structures which make the computation of the matrix R simple and efficient, thereby reducing the number of multiplications in each iteration significantly. As a result we were able to keep the computation time very low. Moreover, use of the resulting structural properties makes the computation of the distribution of queue length of the transformed system efficient. The computation of the distribution of waiting time is also shown to be simple by exploiting the special structures.
- ItemOpen AccessOptimizing radio resources for multicasting on high-altitude platforms(2019-08-29) Ibrahim, Ahmed; Alfa, Attahiru SAbstract High-altitude platforms (HAPs) are quasi-stationary aerial wireless communications platforms meant to be located in the stratosphere, to provide wireless communications and broadband services. They have the ability to fly on demand to temporarily or permanently serve regions with unavailable infrastructure. In this paper, we consider the development of an efficient method for resource allocation and controlling user admissions to multicast groups in a HAP system. Power, frequency, space and time domains are considered in the problem. The combination of these many aspects of the problem in multicasting over an OFDMA HAP system were not, to the best of our knowledge, addressed before. Due to the strong dependence of the total number of users that could join different multicast groups on the possible ways we may allocate resources to the different multicast groups, it is important to consider a joint user to multicast group assignments and radio resource management across the groups. From the service provider’s point of view, it would be in its best interest to be able to admit as many users as possible, while satisfying their quality of service requirements. The problem turns out to be a mixed integer non-convex non-linear program for which branch and bound solution framework is guaranteed to solve the problem. Branch and bound (BnB) can be also used to obtain sub-optimal solutions with desired quality. Even though branch and bound is guaranteed to find the optimal solution, the computational cost could be extremely high, which is why we considered different types of enhancements to BnB. Mainly, we consider reformulations by linearizing a specific set of quadratic constraints in the derived formulation, as well as the application of different branching techniques to find the one that performs the best. Based on the conducted numerical experiments, it was concluded that linearization, applied for at least 100 presolving rounds, and cloud branching achieve the best performance.