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We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and
the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach
the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the
call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per
time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always
sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition.
In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady
state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent
i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence
to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival
and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service
and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential
bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions
for boundedness in distribution for the case of nonpatient (or non persistent) customers.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
Maxim V. Pavlov 《Communications in Mathematical Physics》2007,272(2):469-505
The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. The class of
symmetric hydrodynamic type systems is defined and the calculation of the associated Riemann surfaces is greatly simplified for this
class. Many interesting and physically motivated examples are investigated. 相似文献
5.
A Hamiltonian version has been formulated for the model of axisymmetric equally rotating jet streams with a free boundary. In the framework of this approach, dominant structures, i.e., structure elements appearing in strongly disturbed jet streams at the preturbulent stage of their decay, are studied. It has been shown that compactons, i.e., solution with a compact support, can be such dominant structures. Analysis of the mechanism of the instability of compactons shows the possibility of collapse, which occurs almost without deformation of their shape but leads to the intensification of the vortex sheet at the boundary according to the law (t 0 ? t)?1, where t 0 is the collapse time. 相似文献
6.
We propose iteration methods for solving the Dirichlet problem in domains with involved geometry. Such problems arise in relation to the problem of optimizing quantum dot and antidot infrared detectors. We estimate the deviation of an approximate solution from the exact solution. 相似文献
7.
P. V. Pavlov I. V. Babushkin N. A. Loiko N. N. Rosanov S. V. Fedorov 《Radiophysics and Quantum Electronics》2004,47(10-11):898-904
We consider spatial dissipative solitons arising in the system of two nonlinear thin films which interact resonantly with light. Symmetric and nonsymmetric solitons and methods of their exciting and switching are studied. 相似文献
8.
E. A. Pavlov 《Ukrainian Mathematical Journal》1991,43(1):86-90
A class of singular integral operators is studied from the point of view of the boundedness of their action from some symmetric spaces into other spaces.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 105–110, January, 1991. 相似文献
9.
It is predicted that resonance coupling between two discrete electron energy levels corresponding to different size-quantization
quantum numbers and different Landau quantum numbers can occur in a quantum well in a quantizing magnetic field. The resonance
coupling is due to the interaction of an electron with LO phonons and results in the formation of polaron states of a new type. It is shown that for a certain value of the magnetic
field, which depends on the splitting of the electron size-quantization levels, the absorption peak and the two-phonon resonance
Raman scattering peak split into two components, the separation between which is determined by the electron-phonon coupling
constant. The resonance coupling between size-quantization levels with the same Landau quantum numbers is also studied. The
splitting of the peaks in this case is virtually independent of the magnetic field and can be observed in much weaker fields.
The experimental observation of the effect will make it possible to determine the relative position of the electronic levels
and the electron-phonon coupling constant.
Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 511–515 (10 April 1997) 相似文献
10.