We propose a fluid model driven by the queue length process of a working vacation queue with PH service distribution, which can be applied to the Ad Hoc network with every data group. We obtain the stationary distribution of the queue length in driving process based on a quasi-birth-and-death process. Then, we analyze the fluid model, and derive the differential equations satisfied by the stationary joint distribution of the fluid queue based on the balance equation. Moreover, we obtain some performance indices, such as, the average throughput, server utilization and the mean buffer content. These indices are relevant to pack transmission in the network, and they can be obtained by using the Laplace Transform (LT) and the Laplace-Stieltjes Transform (LST). Finally, some numerical examples have been discussed with respect to the effect of several parameters on the system performance indices.

This paper compares the performance of exhaustive and nonexhaustive M/M/1/N queues with working vacation and threshold policy. In an exhaustive queue, the server slows down its service rate only when no customers exist in the system, and turns to normal service until the number of customers achieves a threshold. However, in a nonexhaustive queue, the server switches service rate between a low and a high value depending on system congestion. To get equilibrium arrival rate of customers and social welfare for the two types of queues, we first derive queue length distributions and expected busy circle. Then, by making sensitivity analysis of busy circle, system cost, arrival rate and optimal social welfare, we find that customers tend to join exhaustive queues instead of nonexhaustive queues, and the optimal threshold in an exhaustive queue is probably inconsistent with the one in a nonexhaustive queue. Moreover, in general, whether to consider system cost or not in social welfare will obviously affect the tendencies of optimal arrival rate and optimal social welfare with the threshold and system capacity for the two types of queues, especially for the nonexhaustive queues, and then affect the final decisions of social planner or system manager.

In this paper, we consider a production inventory system with service time and production vacations. Customers arrive in the system according to a Poisson process requiring service from a single server. The single production facility produces items according to an (s, S) policy, and it takes a vacation of random duration once the inventory level becomes (S. It is assumed that all arriving customers are lost during the stock out period. We first derive the stationary joint distribution of the queue length and the on-hand inventory level in product form. Then, we compute explicitly some performance measures, and develop a cost function based on these performance measures. Finally, some numerical results are presented.

In this paper, we consider an MMPP/M/1/1 retrial queue where incoming fresh calls arrive at the server according to a Markov modulated Poisson process (MMPP). Upon arrival, an incoming call either occupies the server if it is idle or joins a virtual waiting room called orbit if the server is busy. From the orbit, incoming calls retry to occupy the server in an exponentially distributed time and behave the same as a fresh incoming call. After an exponentially distributed idle time, the server makes an outgoing call whose duration is also exponentially distributed but with a different parameter from that of incoming calls. Our contribution is to derive the first order (law of large numbers) and the second order (central limit theorem) asymptotics for the distribution of the number of calls in the orbit under the condition that the retrial rate is extremely low. The asymptotic results are used to obtain the Gaussian approximation for the distribution of the number of calls in the orbit. Our result generalizes earlier results where Poisson input was assumed.

With the rapid growth of energy costs and the constant promotion of environmental standards, energy consumption has become a significant expenditure for the operating and maintaining of a cloud data center. To improve the energy efficiency of cloud data centers, in this paper, we propose a Virtual Machine (VM) scheduling strategy with a speed switch and a multi-sleep mode. In accordance with the current traffic loads, a proportion of VMs operate at a low speed or a high speed, while the remaining VMs either sleep or operate at a high speed. Commensurate with our proposal, we develop a continuous-time queueing model with an adaptive service rate and a partial synchronous vacation. We construct a two dimensional Markov chain based on the total number of requests in the system and the state of all the VMs. Using a matrix geometric solution, we mathematically estimate the energy saving level and the response performance of the system. Numerical experiments with analysis and simulation show that our proposed VM scheduling strategy can effectively reduce the energy consumption without significant degradation in response performance. Additionally, we establish a system utility function to trade off the different performance measures. In order to determine the optimal sleep parameter and the maximum system utility function, we develop an improved Firefly intelligent searching Algorithm.

In this paper, we analyze the performance of a broadcast packet in a VANET with the slotted ALOHA protocol where locations of vehicles are modeled by a one-dimensional Poisson point process. We consider the packet delivery probability under a broadcast delay constraint. Since the successful transmission of a broadcast packet is significantly affected by interferences at receivers which are spatially correlated, it is important to capture the spatial correlations properly in order to obtain an accurate expression of the packet delivery probability in a VANET. However, the exact analysis of the spatial correlations in interference is not mathematically tractable. In this paper we provide an accurate approximation of the spatial correlations in interference and derive the packet delivery probability with the help of the approximation. Numerical and simulation results are provided to validate our analysis and to investigate the performance of a VANET.

Mobile users usually access the Internet via a hybrid access network, in which cellular and Wi-Fi networks are available alternatively. In the hybrid access network, a mobile user decides to send or not to send a packet according to the number of packets already in the system and the phase of the server. In order to evaluate the system performance of the hybrid access network, in this paper we first establish a fully observable continuous time Markovian queueing system. Then, we present an exact analysis to investigate the behavior of the mobile users in the network. Through iterations and diagonalization, we obtain the expected sojourn time of a newly arriving packet in a closed form. Moreover, with the monotonicity for the expected sojourn time of a newly arriving packet, we prove the existence of the Nash equilibrium strategy. Finally, we analyze the socially optimal strategy and motivate the mobile users to accept the socially optimal strategy by changing the sojourn cost.

Service computing is an emerging and distributed computing mode in cloud service systems, and has become an interesting research direction for both academia and industry. Note that the cloud service systems always display new characteristics, such as stochasticity, large scale, loose coupling, concurrency, non-homogeneity and heterogeneity, thus their load balancing investigation has been more interesting, difficult and challenging until now. By using resource management and job scheduling, this paper proposes an integrated, real-time and dynamic control mechanism for large-scale cloud service systems and their load balancing through combining supermarket models with not only work stealing models but also scheduling of public reserved resource. To this end, this paper provides a novel stochastic model with weak interactions by means of nonlinear Markov processes. To overcome theoretical difficulties growing out of the state explosion in high-dimensional stochastic systems, this paper applies the mean-field theory to develop a macro computational technique in terms of an infinite-dimensional system of mean-field equations. Furthermore, this paper proves the asymptotic independence of the large-scale cloud service system, and show how to compute the fixed point by virtue of an infinite-dimensional system of nonlinear equations. Based on the fixed point, this paper provides effective numerical computation for performance analysis of this system under a high approximate precision. Therefore, we hope that the methodology and results given in this paper can be applicable to the study of more general large-scale cloud service systems.