Numeric.Probability.Example.Queuing

Model:

one server serving customers from one queue

Documentation

type Time = Int

type Profile = (Time, Time)

(servingTime, nextArrival)

type Event a = (a, Profile)

type Queue a = [(a, Time)]

customers and their individual serving times

type State a = (Queue a, Time)

(customers waiting,validity period of that queue)

type System a = [([a], Time)]

type Events a = [Event a]

event :: Time -> Events a -> Queue a -> [State a]

system :: Events a -> System a

mEvent :: Int -> Time -> Events a -> Queue a -> [State a]

multiple servers

mServe :: Int -> Int -> Queue a -> Queue a

decrease served customers remaining time by specified amount

mTimeStep :: Int -> Queue a -> Int

time until next completion

mSystem :: Int -> Events a -> System a

random

type RProfile = (Dist Time, Trans Time)

type REvent a = (a, RProfile)

type REvents a = [REvent a]

rSystem :: Int -> REvents a -> T (System a)

rBuildEvents :: REvents a -> T (Events a)

rmSystem :: Ord a => Int -> Int -> REvents a -> RDist (System a)

evalSystem :: (Ord a, Ord b) => Int -> Int -> REvents a -> (System a -> b) -> RDist b

unit :: b -> ((), b)

evaluation

maxQueue :: Ord a => System a -> Int

allWaiting :: Ord a => Int -> System a -> [a]

countWaiting :: Ord a => Int -> System a -> Int

waiting :: Int -> System a -> Time

inSystem :: System a -> Time

total :: System a -> Time

server :: Int -> System a -> Time

idle :: Int -> System a -> Time

idleAvgP :: Int -> System a -> Float