Related papers: Staffing Large Service Systems Under Arrival-rate …
We consider a general queueing system with price-sensitive customers in which the service provider seeks to balance two objectives, maximizing the average revenue rate and minimizing the average queue length. Customers arrive according to a…
Drone delivery systems violate a core assumption in classical queueing models: server capacity is not fixed. Drones (servers) periodically must recharge, creating random fluctuations in service availability. We introduce an Erlang--S$^{*}$…
We study service scheduling problems in a slotted system in which agents arrive with service requests according to a Bernoulli process and have to leave within two slots after arrival, service costs are quadratic in service rates, and there…
Motivated by applications that involve setting proper staffing levels for multi-server queueing systems with batch arrivals, we present a thorough study of the queue-length process $\{Q(t); t \geq 0\}$, departure process $\{D(t); t \geq…
A service system with multiple types of customers, arriving as Poisson processes, is considered. The system has infinite number of servers, ranked by $1,2,3, \ldots$; a server rank is its ``location." Each customer has an independent…
Queues that feature multiple entities arriving simultaneously are among the oldest models in queueing theory, and are often referred to as "batch" (or, in some cases, "bulk") arrival queueing systems. In this work we study the affect of…
A service provisioning system is examined, where a number of servers are used to offer different types of services to paying customers. A customer is charged for the execution of a stream of jobs; the number of jobs in the stream and the…
We study a multiclass M/M/1 queueing control problem with finite buffers under heavy-traffic where the decision maker is uncertain about the rates of arrivals and service of the system and by scheduling and admission/rejection decisions…
This work studies queues in a Euclidean space. Consider $N$ servers that are distributed uniformly in $[0,1]^d$. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide…
We consider a discrete-time system comprising a first-come-first-served queue, a non-preemptive server, and a stationary non-work-conserving scheduler. New tasks enter the queue according to a Bernoulli process with a pre-specified arrival…
In modern computing systems, jobs' resource requirements often vary over time. Accounting for this temporal variability during job scheduling is essential for meeting performance goals. However, theoretical understanding on how to schedule…
We consider a load balancing system consisting of $n$ single-server queues working in parallel, with heterogeneous service rates. Jobs arrive to a central dispatcher, which has to dispatch them to one of the queues immediately upon arrival.…
Let $Q_{\lambda}(t,y) $ be the number of people present at time $t$ with $y$ units of remaining service time in an infinite server system with arrival rate equal to $\lambda>0$. In the presence of a non-lattice renewal arrival process and…
Retailers use a variety of mechanisms to enable sales and delivery. A relatively new offering by companies is curbside pickup where customers purchase goods online, schedule a pickup time, and come to a pickup facility to receive their…
For online resource allocation problems, we propose a new demand arrival model where the sequence of arrivals contains both an adversarial component and a stochastic one. Our model requires no demand forecasting; however, due to the…
A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…
Consider a system of identical server pools where tasks with exponentially distributed service times arrive as a time-inhomogenenous Poisson process. An admission threshold is used in an inner control loop to assign incoming tasks to server…
We present a new framework for designing nonpreemptive and job-size oblivious scheduling policies in the multiserver-job queueing model. The main requirement is to identify a static and balanced sub-partition of the server set and ensure…
This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements and the server work rate are modulated by a general c\`{a}dl\`{a}g stochastic background process. To prove a large…
5G and beyond networks are expected to support flows with varied \emph{Quality-of-Service (QoS)} requirements under unpredictable traffic conditions. Consequently, designing policies ensuring optimal system utilization in such networks is…