General expressions of first passage times for denumerable Markov processes are discussed and computation problems for busy periods and waiting times for queues corresponding to Markov processes are studied. In partic...General expressions of first passage times for denumerable Markov processes are discussed and computation problems for busy periods and waiting times for queues corresponding to Markov processes are studied. In particular, the simplified algorithms for busy periods and waiting times for queues corresponding to G//M/1 type and M/G/1 type Markov processes are derived and some numerical examples are presented.展开更多
This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vect...This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical experiment to implement the proposed algorithm.展开更多
An upper bound is established on the parameter Γ -(G) for a cubic graph G and two infinite families of 3-connected graphs G k, G * k are constructed to show that the bound is sharp and, moreover, the difference Γ -(...An upper bound is established on the parameter Γ -(G) for a cubic graph G and two infinite families of 3-connected graphs G k, G * k are constructed to show that the bound is sharp and, moreover, the difference Γ -(G * k)-γ s(G * k) can be arbitrarily large, where Г -(G * k) and γ s(G * k) are the upper minus domination and signed domination numbers of G * k, respectively. Thus two open problems are solved.展开更多
基金the National Natural Science Foundation of China
文摘General expressions of first passage times for denumerable Markov processes are discussed and computation problems for busy periods and waiting times for queues corresponding to Markov processes are studied. In particular, the simplified algorithms for busy periods and waiting times for queues corresponding to G//M/1 type and M/G/1 type Markov processes are derived and some numerical examples are presented.
文摘This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical experiment to implement the proposed algorithm.
文摘An upper bound is established on the parameter Γ -(G) for a cubic graph G and two infinite families of 3-connected graphs G k, G * k are constructed to show that the bound is sharp and, moreover, the difference Γ -(G * k)-γ s(G * k) can be arbitrarily large, where Г -(G * k) and γ s(G * k) are the upper minus domination and signed domination numbers of G * k, respectively. Thus two open problems are solved.
