From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deri...

We consider the FCFS GI/GI/n queue in the Halfin-Whitt heavy traffic regime, and prove bounds for the steady-state probability of delay (s.s.p.d.) for generally distributed processing times. We prove that there exists ε > 0, depending on the inter-arrival and processing time distributions, such that the s.s.p.d. is bounded from above by exp ( − εB ) as the associated excess parameter B →∞; and ...

This paper uses a unique data set of linked employer-employee data in which asset transfers between firms can be identified to study the manner in which employment policy changes in the aftermath of a merger or acquisition (M&A). Using parametric duration models with unobserved heterogeneity and modeling the status of the employer with respect to M&A activity, it appear that the employment poli...

In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t) + a with probability 1 − ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, w...

A Fokker-Planck formulation of systems described by stochastic delay differential equations has been recently proposed. A separation of time scales approximation allowing this Fokker-Planck equation to be simplified in the case of multistable systems is hereby introduced, and applied to a system consisting of a particle coupled to a delayed quartic potential. In that approximation, population n...

Inelastic collapse has been observed in a wide range of granular simulations. Very little work, however, has been done in the area of detection of inelastic collapse in couette flow hard sphere simulations. Only recently has the occurrence of inelastic collapse been investigated for such systems. That work has shown that the probability of detecting inelastic collapse increases with a decrease ...

In this paper, a multi phase M/G/1queueing system with Bernoulli feedback where the server takes multiple vacation is considered. All the poisson arrivals with mean arrival rate will demand any of the multi essential services.. The service times of the first essential service are assumed to follow a general distribution Bi(v). After the completion of any of the n services, if the customer is di...

We study the steady state of the abelian sandpile models with stochastic toppling rules. The particle addition operators commute with each other, but in general these operators need not be diagonalizable. We use their abelian algebra to determine their eigenvalues, and the Jordan block structure. These are then used to determine the probability of different configurations in the steady state. W...

Three models of surface growth processes in nonequilibrium steady state (NESS): Edwards–Wilkinson Model, Mullins–Herring Model and Kardar–Parisi–Zhang Model, are presented. Power laws, universality of non-equilibrium distributions, and scaling functions are discussed in details together with some experiment results.

The paging signaling overhead is occurred in Paging extensions for Mobile IP(P-MIP) which was proposed to reduce registration signaling overhead of Mobile IP(MIP). And quick paging IP scheme using residence pattern of mobile user(QP-MIP) is proposed to overcome the above inefficiency. To the exact analysis of QP-MIP and P-MIP, the Mobile Node(MN) state transition behavior is modeled and the ste...