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The growth of Machine-Type Communication (MTC) increases the relevance of queuing scenarios with deterministic service times. In this letter, we present a model for queues without waiting lines and with degenerate service time distributions…
Finite-capacity single-server queues with general service-time distributions form the backbone of numerous real-world systems, yet classical simulation of performance metrics such as blocking probabilities and delay becomes computationally…
This paper studies an infinite buffer single server queueing model with exponentially distributed service times and negative arrivals. The ordinary (positive) customers arrive in batches of random size according to renewal arrival process,…
To mimic the complex transport-like collective phenomena in a man-made or natural system, we study an open network junction model of totally asymmetric simple exclusion process with bulk particle attachment and detachment. The stationary…
We introduce the {\Delta}(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F. Thus, the arrival times are an ordered statistics, and the…
The non-stationary Erlang-A queue is a fundamental queueing model that is used to describe the dynamic behavior of large scale multi-server service systems that may experience customer abandonments, such as call centers, hospitals, and…
Scaling transformations involving a small parameter ({\em degenerate scalings}) are frequently used for ordinary differential equations that model (bio-) chemical reaction networks. They are motivated by quasi-steady state (QSS) of certain…
We consider a model for a queue in which only a fixed number $N$ of customers can join. Each customer joins the queue independently at an exponentially distributed time. Assuming further that the service times are independent and follow an…
We study the performance of random linear network coding for time division duplexing channels with Poisson arrivals. We model the system as a bulk-service queue with variable bulk size. A full characterization for random linear network…
We consider a single server system with infinite waiting room in a random environment. The service system and the environment interact in both directions. Whenever the environment enters a prespecified subset of its state space the service…
We address the problem of giving robust performance bounds based on the study of the asymptotic behavior of the insensitive load balancing schemes when the number of servers and the load scales jointly. These schemes have the desirable…
The collective motion of interacting self-driven particles describes many types of coordinated dynamics and self-organisation. Prominent examples are alignment or lane formation which can be observed alongside other ordered structures and…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
In the Hammersley-Aldous-Diaconis process infinitely many particles sit in R and at most one particle is allowed at each position. A particle at x$ whose nearest neighbor to the right is at y, jumps at rate y-x to a position uniformly…
We consider a two-queue polling model with switch-over times and $k$-limited service (serve at most $k_i$ customers during one visit period to queue $i$) in each queue. The major benefit of the $k$-limited service discipline is that it -…
We analyse time evolution of spread complexity (SC) in an isolated interacting quantum many-body system when it is subjected to a sudden quench. The differences in characteristics of the time evolution of the SC for different time scales is…
We consider an infinite server queue where the arrival and the service rates are both modulated by a stochastic environment governed by an $S$-valued stochastic process $X$ that is ergodic with a limiting measure $\pi\in \mathcal{P}(S)$.…
We study a queueing system with Poisson arrivals on a bus line indexed by integers. The buses move at constant speed to the right and the time of service per customer getting on the bus is fixed. The customers arriving at station i wait for…
One of the key performance measures in queueing systems is the exponential decay rate of the steady-state tail probabilities of the queue lengths. It is known that if a corresponding fluid model is stable and the stochastic primitives have…
A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling and routing,…