Markov modulated fluid network process: Tail asymptotics of the stationary distribution

Tail asymptotics of a Markov-modulated infinite-server queue

This paper analyzes large deviation probabilities related to the number of customers in a Markov modulated infinite-server queue, with state-dependent arrival and service rates. Two specific scalings are studied: in the first, just the arrival rates are linearly scaled by N (for large N ), whereas in the second in addition the Markovian background process is sped up by a factor N , for some > 0...

Join the shortest queue among $$k$$ parallel queues: tail asymptotics of its stationary distribution

We are concerned with an M/M -type join the shortest queue (M/M -JSQ for short) with k parallel queues for an arbitrary positive integer k, where the servers may be heterogeneous. We are interested in the tail asymptotic of the stationary distribution of this queueing model, provided the system is stable. We prove that this asymptotic for the minimum queue length is exactly geometric, and its d...

Markov Modulated Linear Fluid

Markov Modulated Linear Fluid

Conjectures on tail asymptotics of the marginal stationary distribution for a multidimensional SRBM

We are concerned with the stationary distribution of a d-dimensional semimartingale reflecting Brownian motion on a nonnegative orthant, provided it is stable, and conjecture about the tail decay rate of its marginal distribution in an arbitrary direction. Due to recent studies, the conjecture is true for d = 2. We show its validity for the skew symmetric case for a general d .