In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matr...In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function（PGF） of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X]/M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.展开更多
SnO 2 nanospheres with diameters of 30∼50 nm and Pt x Cu 1-x bimetallic nanoparticles with sizes of approxi-mately 10 nm were synthesized via hydrothermal and solvothermal methods,respectively.The Pt x Cu 1-x bimetal...SnO 2 nanospheres with diameters of 30∼50 nm and Pt x Cu 1-x bimetallic nanoparticles with sizes of approxi-mately 10 nm were synthesized via hydrothermal and solvothermal methods,respectively.The Pt x Cu 1-x bimetal-lic nanoparticles were impregnated on the surface of the SnO 2 spheres to form Pt x Cu 1-x-SnO 2 nanocomposites.By varying the atomic ratios between platinum(Pt)and copper(Cu),we found that Pt 0.75 Cu 0.25-SnO 2,with a large specific surface area of 89.21 m 2/g,enabled the selective and accurate detection of low-concentration formalde-hyde compared to other metal-deposited samples and pure SnO 2.The response value of Pt 0.75 Cu 0.25-SnO 2 to 500×10−9 formaldehyde was approximately 20 at an operating temperature of 160◦C with an extremely high-speed response(15 s).The porous structures with large specific surface areas,as well as the improved catalytic effects of Pt 0.75 Cu 0.25,comprehensively contributed to the enhanced sensing performance towards formaldehyde.展开更多
基金supported by National Natural Science Foundation of China(No. 10671170)Natural Science Foundation of Hebei Province(No. F2008000864)
文摘In this paper, we analyze a bulk input M^[X]/M/1 queue with multiple working vacations. A quasi upper triangle transition probability matrix of two-dimensional Markov chain in this model is obtained, and with the matrix analysis method, highly complicated probability generating function（PGF） of the stationary queue length is firstly derived, from which we got the stochastic decomposition result for the stationary queue length which indicates the evident relationship with that of the classical M^[X]/M/1 queue without vacation. It is important that we find the upper and the lower bounds of the stationary waiting time in the Laplace transform order using the properties of the conditional Erlang distribution. Furthermore, we gain the mean queue length and the upper and the lower bounds of the mean waiting time.
基金This study was supported by the Natural Science Foundation of Shan-dong Province(No.ZR2019QF012)the Natural Science and Develop-ment Foundation of Shenzhen(JCYJ20190807093205660)the Na-tional Natural Science Foundation of China(No.21902085).
文摘SnO 2 nanospheres with diameters of 30∼50 nm and Pt x Cu 1-x bimetallic nanoparticles with sizes of approxi-mately 10 nm were synthesized via hydrothermal and solvothermal methods,respectively.The Pt x Cu 1-x bimetal-lic nanoparticles were impregnated on the surface of the SnO 2 spheres to form Pt x Cu 1-x-SnO 2 nanocomposites.By varying the atomic ratios between platinum(Pt)and copper(Cu),we found that Pt 0.75 Cu 0.25-SnO 2,with a large specific surface area of 89.21 m 2/g,enabled the selective and accurate detection of low-concentration formalde-hyde compared to other metal-deposited samples and pure SnO 2.The response value of Pt 0.75 Cu 0.25-SnO 2 to 500×10−9 formaldehyde was approximately 20 at an operating temperature of 160◦C with an extremely high-speed response(15 s).The porous structures with large specific surface areas,as well as the improved catalytic effects of Pt 0.75 Cu 0.25,comprehensively contributed to the enhanced sensing performance towards formaldehyde.
