Queueing Systems

Let $$\xi _1,\xi _2,\ldots $$ξ1,ξ2,… be independent, identically distributed random variables with infinite mean $${\mathbf {E}}[|\xi _1|]=\infty .$$E[|ξ1|]=∞. Consider a random walk $$S_n=\xi _1+\cdots +\xi _n$$Sn=ξ1+⋯+ξn, a stopping time $$\tau …

Many service systems use technology to notify customers about their expected waiting times or queue lengths via delay announcements. However, in many cases, either the information might be delayed or customers might require time to travel to the …

Bulk-service multi-server queues with heterogeneous server capacity and thresholds are commonly seen in several situations such as passenger transport or package delivery services. In this paper, we develop a novel decomposition-based solution …

We consider Poisson streams of exponentially distributed jobs arriving at each edge of a hypergraph of queues. Upon arrival, an incoming job is routed to the shortest queue among the corresponding vertices. This generalizes many known models such …

Donsker’s theorem is perhaps the most famous invariance principle result for Markov processes. It states that, when properly normalized, a random walk behaves asymptotically like a Brownian motion. This approach can be extended to general Markov …