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A convergence theorem for controlled queues with partial observations

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Priority queue

In computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure. Each element in a priority queue has an associated priority. In a priority queue, elements with high priority are served before elements with low priority. In some implementations, if two elements have the same priority, they are served in the same order in which they were enqueued. In other implementations, the order of elements with the same priority is undefined.

Network scheduler

A network scheduler, also called packet scheduler, queueing discipline (qdisc) or queueing algorithm, is an arbiter on a node in a packet switching communication network. It manages the sequence of network packets in the transmit and receive queues of the protocol stack and network interface controller. There are several network schedulers available for the different operating systems, that implement many of the existing network scheduling algorithms. The network scheduler logic decides which network packet to forward next.

Monotone convergence theorem

In the mathematical field of real analysis, the monotone convergence theorem is any of a number of related theorems proving the convergence of monotonic sequences (sequences that are non-decreasing or non-increasing) that are also bounded. Informally, the theorems state that if a sequence is increasing and bounded above by a supremum, then the sequence will converge to the supremum; in the same way, if a sequence is decreasing and is bounded below by an infimum, it will converge to the infimum.

Scheduling (computing)

In computing, scheduling is the action of assigning resources to perform tasks. The resources may be processors, network links or expansion cards. The tasks may be threads, processes or data flows. The scheduling activity is carried out by a process called scheduler. Schedulers are often designed so as to keep all computer resources busy (as in load balancing), allow multiple users to share system resources effectively, or to achieve a target quality-of-service.

Interest rate

An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, deposited, or borrowed. The annual interest rate is the rate over a period of one year. Other interest rates apply over different periods, such as a month or a day, but they are usually annualized.

Pushforward measure

In measure theory, a pushforward measure (also known as push forward, push-forward or image measure) is obtained by transferring ("pushing forward") a measure from one measurable space to another using a measurable function. Given measurable spaces and , a measurable mapping and a measure , the pushforward of is defined to be the measure given by for This definition applies mutatis mutandis for a signed or complex measure. The pushforward measure is also denoted as , , , or .

Convergence of random variables

In probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied.

Packet loss

Packet loss occurs when one or more packets of data travelling across a computer network fail to reach their destination. Packet loss is either caused by errors in data transmission, typically across wireless networks, or network congestion. Packet loss is measured as a percentage of packets lost with respect to packets sent. The Transmission Control Protocol (TCP) detects packet loss and performs retransmissions to ensure reliable messaging.

Markov model

In probability theory, a Markov model is a stochastic model used to model pseudo-randomly changing systems. It is assumed that future states depend only on the current state, not on the events that occurred before it (that is, it assumes the Markov property). Generally, this assumption enables reasoning and computation with the model that would otherwise be intractable. For this reason, in the fields of predictive modelling and probabilistic forecasting, it is desirable for a given model to exhibit the Markov property.

Queuing delay

In telecommunication and computer engineering, the queuing delay or queueing delay is the time a job waits in a queue until it can be executed. It is a key component of network delay. In a switched network, queuing delay is the time between the completion of signaling by the call originator and the arrival of a ringing signal at the call receiver. Queuing delay may be caused by delays at the originating switch, intermediate switches, or the call receiver servicing switch.