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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.

A discrete time Geo/Geo/1 queue with (m, N)-policy is considered in this paper. There are three operation periods being considered: high speed, low speed service periods and idle periods. With double thresholds policy, the server begins to take a working vacation when the number of customers is below m after a service and there is one customer in the system at least. What’s more, if the system becomes empty after a service, the server will take an ordinary vacation. Otherwise, high speed service continues if the number of customers still exceeds m after a service. At the vacation completion instant, servers resume their service if the quantity of customers exceeds N. Vacations can also be interrupted when the system accumulate customers more than the prefixed threshold. Using the quasi birth-death process and matrix-geometric solution methods, we derive the stationary queue length distribution and some system characteristics of interest. Based on these, we apply the queue to a virtual channel switching system and present various numerical experiments for the system. Finally, numerical results are offered to illustrate the optimal (m, N)-policy to minimize cost function and obtain practical consequence on the operation of double thresholds policy.

A novel electrode material of polyaniline/HF partially etched-hierarchical porous TiO2 microspheres (PANI/F-HPTM) composite has been designed and synthesized by the combination of graft polymerization of PANI on the surface of HPTM and subsequent partially etch HPTM using HF. The preparation process is systematically investigated by Fourier transform infrared spectroscopy (FTIR), energy-dispersive spectroscopy analysis (EDS), and X-ray diffraction (XRD). The surface morphology is examined by field-emission scanning electron microscopy (FESEM). The capacitive behaviors are characterized by cyclic voltammetry (CV) and galvanostatic charge-discharge (GCD). The unique structure design and partially etched strategy make the composite exhibits desirable electrochemical performance. The maximum specific capacitance of PANI/F-HPTM is 497.6 F g−1 at a current density of 0.7 A g−1, and the specific capacitance retention rate is 81.1 % as the current density increasing from 0.7 A to 14 A g−1. In addition, almost 100 % of its initial specific capacitance can retain after charge/discharge for 1000 cycles. These results demonstrate that partial etching is a good strategy and HPTM are promising templates to prepare high-performance electrode materials for supercapacitors.