# American Institute of Mathematical Sciences

ISSN:
1547-5816

eISSN:
1553-166X

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## Journal of Industrial & Management Optimization

2011 , Volume 7 , Issue 3

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2011, 7(3): 523-529 doi: 10.3934/jimo.2011.7.523 +[Abstract](413) +[PDF](257.8KB)
Abstract:
In this paper, we point out some errors in a recent paper of M.A.E.H.Kassen (Applied Mathematics and Computation 183(2006) 1121-1126). And a pair of the first-order symmetric dual model for vector optimization problem is proposed in this paper. Then, we prove the weak, strong and converse duality theorems for the formulated first-order symmetric dual programs under invexity conditions.
2011, 7(3): 531-558 doi: 10.3934/jimo.2011.7.531 +[Abstract](529) +[PDF](731.7KB)
Abstract:
This paper proposes an application of data envelopment analysis (DEA) to measure the value of customers. In order to distinguish between expectations and needs of profitable and unprofitable customers and to allocate marketing investments among them, customers are compared with each other and ranked in a customer value pyramid. To this end, we use a combination of the Banker, Charnes and Cooper (BCC) model [3], assurance region (AR) model, and cross-efficiency evaluation. A numerical example demonstrates the application of the proposed model in an Iranian manufacturing company.
2011, 7(3): 559-571 doi: 10.3934/jimo.2011.7.559 +[Abstract](387) +[PDF](355.3KB)
Abstract:
In this paper, for a class of weak bilevel programming problems we provide sufficient conditions guaranteeing the existence of global solutions. These conditions are based on the use of reverse convex and convex maximization problems.
2011, 7(3): 573-592 doi: 10.3934/jimo.2011.7.573 +[Abstract](446) +[PDF](497.6KB)
Abstract:
This paper undertakes a three-stage DEA-SFA (Data Envelopment Analysis / Stochastic Frontier Analysis) efficiency analysis of labour-owned (LOF) and mercantile (PCF) firms to assess whether variations in the productive efficiency and in the total factor productivity of LOFs and PCFs are explainable by differences in their capital-ownership configuration. The model first purges, from each firm's performance, the impact of statistical noise and of environmental factors and yields increasing average efficiency estimates of the firms under study. Then, it tests the hypothesis that the average firm, be it LOF or PCF, is equally efficient and exhibits comparable levels of productivity growth. The evidence presented supports the proposition that differences in the capital-ownership configuration do not play a very significant role in their performance efficiency or in their productivity growth and whatever productivity growth occurs is attributable largely to innovation rather than to catching up to the efficient firms.
2011, 7(3): 593-606 doi: 10.3934/jimo.2011.7.593 +[Abstract](441) +[PDF](434.0KB)
Abstract:
In this paper, we consider an $M/M/s$ queueing model where customers may abandon waiting for service and leave the system without receiving their services. We assume that impatient time on waiting for each customer is an independent and identically distributed nonnegative random variable with a general distribution where the probability distribution is light-tailed and unbounded. The main objective of this paper is to provide an approximation for the waiting time distribution in an analytically tractable form. To this end, we obtain the tail asymptotics of the waiting time distributions of served and impatient customers. By using the tail asymptotics, we show that the fairly good approximations of the waiting time distributions can be obtained in asymptotic region with low numerical complexity.
2011, 7(3): 607-622 doi: 10.3934/jimo.2011.7.607 +[Abstract](372) +[PDF](408.3KB)
Abstract:
In this paper, we consider a wireless network consisting of a source node, a destination node and multiple relay nodes under Rayleigh fading. Cooperative diversity in the network is achieved by selecting an opportunistic relay node with the best channel condition to the destination node. We focus on the packet level performance in this paper and analyze the average packet delay of the network for various modulation and coding schemes. We assume that the arrival process of packets follows a Markov modulated Poisson process (MMPP). To derive the average packet delay, we first derive the distribution of the number of packets that are successfully transmitted from the source node to the destination node via a relay node. Using the distribution obtained above, a queueing process of the M/G/1 type is developed to model the queue at the source node. The average packet delay is then obtained from the stationary distribution of the queueing process of the source node by applying Little's Lemma. Based on our results on the average packet delay, the optimal modulation and coding scheme for given network parameters is determined to minimize the average packet delay. We validate our analytic model through simulation. The detailed relations between the average packet delay and network parameters such as average signal to noise ratios (SNRs) between nodes, the number of relay nodes and packet arrival rate, are investigated through numerical studies based on our analytic model as well as simulation studies. From our numerical results, we conclude that the optimal modulation and coding scheme that minimizes the average packet delay depends not only on SNRs of channels between nodes but also on the arrival rate of packets at the data link layer.
2011, 7(3): 623-639 doi: 10.3934/jimo.2011.7.623 +[Abstract](302) +[PDF](413.7KB)
Abstract:
Power saving is one of the important issues for battery-powered mobile station in mobile WiMAX. Both IEEE 802.16e and IEEE 802.16m standards define sleep mode operations for power saving of mobile stations. In this paper, we propose an efficient sleep mode operation for the IEEE 802.16m advanced mobile WiMAX. The proposed scheme takes advantages of sleep modes in both the IEEE 802.16e and IEEE 802.16m. This scheme has binary exponential sleep windows which guarantee the minimum length for effective power saving. The mobile station uses the T_AMS timer in the IEEE 802.16m so that the mobile station sends or receives data packets during the extendable listening window in the sleep mode. We mathematically analyze the proposed scheme by an embedded Markov chain to obtain the average message delay and the average power consumption of a mobile station. The analytical results match with the simulation results very well. The analytical results show that the power consumption of our scheme is better than those of the legacy sleep modes in the IEEE 802.16e and the IEEE 802.16m under the same delay bound.
2011, 7(3): 641-653 doi: 10.3934/jimo.2011.7.641 +[Abstract](309) +[PDF](365.7KB)
Abstract:
In this paper, we present a Geom/Geom/1 queueing model with variable input probability. In this queueing model, an arriving customer, who sees many customers waiting for service in the queueing system, will consider whether to enter the system or not. We consider the possibility that the customer enters the system to receive service to be a probability called the "Input Probability". We derive the transition probability matrix of the birth and death chain of the queueing model. Using a birth and death process, we gain the probability distributions of the stationary queue length and the waiting time in the queueing model. Then we derive special cases of the considered model by applying different input probability distributions, which lead to several known specific queueing models. We also derive some performance measures of these specific queueing models. Therefore, this queueing model that we present in this paper has a certain extension, extending to the existing models. Finally, we compare the effect of the parameters on the stationary queue length and waiting time by using numerical results.
2011, 7(3): 655-676 doi: 10.3934/jimo.2011.7.655 +[Abstract](362) +[PDF](267.2KB)
Abstract:
This paper is concerned with the queueing analysis as well as reliability evaluation of an $M/G/1//K$ retrial queue with a finite number of sources in which the server is subject to breakdowns and repairs. The server has a exponentially distributed life time and a generally distributed repair time. Our analysis extends previous work on this topic and includes the analysis of the arriving customer's distribution, the busy period, the waiting time process and main reliability characteristics. This queueing system and its variants could be used to model magnetic disk memory systems, star-like local area networks and other communication systems with detected or undetected breakdowns.
2011, 7(3): 677-697 doi: 10.3934/jimo.2011.7.677 +[Abstract](350) +[PDF](507.6KB)
Abstract:
In this paper we introduce the globally gated Markovian limited service discipline in the cyclic polling model. Under this policy at most K customers are served during the server visit to a station among the customers that are present at the start of the actual polling cycle. Here the random limit K is the actual value of a finite state Markov chain assigned to the actual station. The model enables asymmetric Poisson arrival flows and each station has an individual Markov chain. This model is analyzed and the numerical solution for the mean of the stationary waiting time is provided.
This model is motivated by the problem of dynamic capacity allocation in Media Access Control of wireless communication networks with Time-Division Multiple Access mechanism. The "globally gated" character of the model is the consequence of the applied reservation mechanisms. In a fixed length frame after allocating the required capacity for the delay sensitive real-time traffic the random remaining capacity is shared among the subscriber stations for the non real-time traffic. The Markovian character of the random limits enables to model the inter frame dependencies of the required real-time capacity at each station individually.
In the second part of the paper the application of this model to the uplink traffic in the IEEE 802.16 network is discussed.
2011, 7(3): 699-716 doi: 10.3934/jimo.2011.7.699 +[Abstract](395) +[PDF](754.2KB)
Abstract:
In a Peer-to-Peer (P2P) based video streaming system such as Coolstreaming, a single video stream is decomposed into multiple sub-streams. A client-peer node receives the sub-streams from multiple parent-peer nodes, combining them into the original video stream. Each client-peer node has a synchronization buffer and a cache buffer. Data blocks are stored in the synchronization buffer in a sub-stream basis, and then forwarded into the cache buffer according to their sequence numbers. In this buffering system, data-block synchronization plays a crucial role to guarantee video quality. In this paper, we consider the performance of data-block synchronization scheme with which data blocks are simultaneously forwarded just after all the data blocks composing a macro data block arrive at the synchronization buffer. We model the synchronization buffer as a multiple-buffer queueing system with homogeneous Poisson arrival processes, deriving the mean forwarding interval. We also consider the frame loss probability for multiple-path video streaming, investigating how the number of sub-streams decreases the frame loss probability. Numerical examples show that increasing the number of sub-streams makes the average forwarding interval large, while the frame loss probability at the bottleneck router is improved. It is also shown that increasing the synchronization buffer decreases the average forwarding interval.
2011, 7(3): 717-733 doi: 10.3934/jimo.2011.7.717 +[Abstract](411) +[PDF](455.5KB)
Abstract:
One of the most important ways for extending the battery lifetime of Mobile Stations (MSs) in a wireless Metropolitan Area Network (MAN) is to conserve the power consumption effectively. When a power saving mechanism with the sleep mode in IEEE 802.16-2009 is used, the system will be in a sleep state and the energy will be saved if both the Uplink (UL) and the Downlink (DL) are idle. In this paper, we present a new mathematical analysis for the system model with synchronous multiple vacations to capture the working principle of the Power Saving Class (PSC) type III in IEEE 802.16-2009 by taking into account the bi-directional traffic (the UL traffic and DL traffic together). By using the methods of a semi-Markov process and a two-dimensional embedded Markov chain, we derive the steady-state probability distribution of the system. Noting that the transmission of UL data frame will not be influenced by the sleep mode, but the sleep mode can be terminated by the arrival of UL data frames, we give the formula for the average delay of the DL data frames taking the bi-directional traffic into consideration. Moreover, we also present the expression for the energy saving ratio. Analytical results and simulation results are provided to investigate and validate the influence of the system parameters on the system performance. Finally, considering the trade-off between the average delay of data frames and the energy saving ratio, we develop a cost function to determine the optimal length of the sleep window in order to maximize the energy saving ratio while satisfying the Quality of Service (QoS) constraint on the average delay of data frames.
2011, 7(3): 735-751 doi: 10.3934/jimo.2011.7.735 +[Abstract](392) +[PDF](544.2KB)
Abstract:
This paper studies a finite-sized discrete-time two-class priority queue. Packets of both classes arrive according to a two-class discrete batch Markovian arrival process (2-DBMAP), taking into account the correlated nature of arrivals in heterogeneous telecommunication networks. The model incorporates time and space priority to provide different types of service to each class. One of both classes receives absolute time priority in order to minimize its delay. Space priority is implemented by the partial buffer sharing acceptance policy and can be provided to the class receiving time priority or to the other class. This choice gives rise to two different queueing models and this paper analyses both these models in a unified manner. Furthermore, the buffer finiteness and the use of space priority raise some issues on the order of arrivals in a slot. This paper does not assume that all arrivals from one class enter the queue before those of the other class. Instead, a string representation for sequences of arriving packets and a probability measure on the set of such strings are introduced. This naturally gives rise to the notion of intra-slot space priority. Performance of these queueing systems is then determined using matrix-analytic techniques. The numerical examples explore the range of service differentiation covered by both models.
2011, 7(3): 753-765 doi: 10.3934/jimo.2011.7.753 +[Abstract](461) +[PDF](226.3KB)
Abstract:
We consider a retrial queueing network with different classes of customers and several servers. Each customer class is associated with a set of servers who can serve the class of customers. Customers of each class exogenously arrive according to a Poisson process. If an exogenously arriving customer finds upon his arrival any idle server who can serve the customer class, then he begins to receive a service by one of the available servers. Otherwise he joins the retrial group, and then tries his luck again after exponential time, the mean of which is determined by his customer class. Service times of each server are assumed to have general distribution. The retrial queueing network can be represented by a Markov process, with the number of customers of each class, and the customer class and the remaining service time of each busy server. Using the fluid limit technique, we find a necessary and sufficient condition for the positive Harris recurrence of the representing Markov process. This work is the first that applies the fluid limit technique to a model with retrial phenomena.
2011, 7(3): 767-788 doi: 10.3934/jimo.2011.7.767 +[Abstract](383) +[PDF](432.2KB)
Abstract:
A well-known problem with priority policies is starvation of delay-tolerant traffic. Additionally, insufficient control over delay differentiation (which is needed for modern network applications) has incited the development of sophisticated scheduling disciplines. The priority policy we present here has the benefit of being open to rigorous analysis. We study a discrete-time queueing system with a single server and single queue, in which $N$ types of customers enter pertaining to different priorities. A general i.i.d. arrival process is assumed and service times are generally distributed. We divide the time axis into 'frames' of fixed size (counted as a number of time-slots), and reorder the customers that enter the system during the same frame such that the high-priority customers are served first. This paper gives an analytic approach to studying such a system, and in particular focuses on the system content (meaning the customers of each type in the system at random slotmarks) in stationary regime, and the delay distribution of a random customer. Clearly, in such a system the frame's size is the key factor in the delay differentiation between the $N$ priority classes. The numerical results at the end of this paper illustrate this observation.

2017  Impact Factor: 0.994