1,925 research outputs found
Invariance of fluid limits for the Shortest Remaining Processing Time and Shortest Job First policies
We consider a single-server queue with renewal arrivals and i.i.d. service
times, in which the server employs either the preemptive Shortest Remaining
Processing Time (SRPT) policy, or its non-preemptive variant, Shortest Job
First (SJF). We show that for given stochastic primitives (initial condition,
arrival and service processes), the model has the same fluid limit under either
policy. In particular, we conclude that the well-known queue length optimality
of preemptive SRPT is also achieved, asymptotically on fluid scale, by the
simpler-to-implement SJF policy. We also conclude that on fluid scale, SJF and
SRPT achieve the same performance with respect to response times of the
longest-waiting jobs in the system.Comment: 24 page
On the Gittins index in the M/G/1 queue
For an M/G/1 queue with the objective of minimizing the mean number of jobs in the system, the Gittins index rule is known to be optimal among the set of non-anticipating policies. We develop properties of the Gittins index. For a single-class queue it is known that when the service time distribution is of type Decreasing Hazard Rate (New Better than Used in Expectation), the Foreground-Background (First-Come-First-Served) discipline is optimal. By utilizing the Gittins index approach, we show that in fact, Foreground-Background and First-Come-First-Served are optimal if and only if the service time distribution is of type Decreasing Hazard Rate and New Better than Used in Expectation, respectively. For the multi-class case, where jobs of different classes have different service distributions, we obtain new results that characterize the optimal policy under various assumptions on the service time distributions. We also investigate distributions whose hazard rate and mean residual lifetime are not monotonic. © Springer Science+Business Media, LLC 2009
Priority Auctions and Queue Disciplines that Depend on Processing Time
Lecture on the first SFB/TR 15 meeting, Gummersbach, July, 18 - 20, 2004We analyze the allocation of priority in queues via simple bidding mechanisms. In our model, the stochastically arriving customers are privately informed about their own processing time. They make bids upon arrival at a queue whose length is unobservable. We consider two bidding schemes that differ in the definition of bids (these may reflect either total payments or payments per unit of time) and in the timing of payments (before, or after service). In both schemes, a customer obtains priority over all customers (waiting in the queue or arriving while he is waiting) who make lower bids. Our main results show how the convexity/concavity of the function expressing the costs of delay determines the queue-discipline (i.e., SPT, LPT) arising in a bidding equilibrium
Priority Auctions and Queue Disciplines that Depend on Processing Time
Lecture on the first SFB/TR 15 meeting, Gummersbach, July, 18 - 20, 2004We analyze the allocation of priority in queues via simple bidding mechanisms. In our model, the stochastically arriving customers are privately informed about their own processing time. They make bids upon arrival at a queue whose length is unobservable. We consider two bidding schemes that differ in the definition of bids (these may reflect either total payments or payments per unit of time) and in the timing of payments (before, or after service). In both schemes, a customer obtains priority over all customers (waiting in the queue or arriving while he is waiting) who make lower bids. Our main results show how the convexity/concavity of the function expressing the costs of delay determines the queue-discipline (i.e., SPT, LPT) arising in a bidding equilibrium.
Age-Optimal Updates of Multiple Information Flows
In this paper, we study an age of information minimization problem, where
multiple flows of update packets are sent over multiple servers to their
destinations. Two online scheduling policies are proposed. When the packet
generation and arrival times are synchronized across the flows, the proposed
policies are shown to be (near) optimal for minimizing any time-dependent,
symmetric, and non-decreasing penalty function of the ages of the flows over
time in a stochastic ordering sense
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