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scalation/scalation/scalation.simulation/scalation.simulation.queueingnet/MM_Queue

MM_Queue

scalation.simulation.queueingnet.MM_Queue
trait MM_Queue(λ: Double, μ: Double, c: Int)

The MM_Queue trait is used to solve single node Markovian Queueing problems. It models a service station consisting of one queue and c servers. The arrivals are Poisson and the service time distribution is Exponential.

Value parameters

λ

the overall arrival rate (lambda)

μ

the per unit service rate (mu)

Attributes

See also

also MMck_Queue to model finite capacity queues.

Graph
Supertypes
class Object
trait Matchable
class Any
Known subtypes
class MM1_Queue
class MM2_Queue
class MMc_Queue
class MGc_Queue
class MMck_Queue

Members list

Value members

Abstract methods

def `π_0`: Double

Probability the system is empty (in state 0, no entities).

Probability the system is empty (in state 0, no entities).

Attributes

def l_y: Double

Concrete methods

def `π_k`: Double

Probability the system is full (in state k where k is the capacity). For infinite capacity queues, it is 0. Override as needed.

Probability the system is full (in state k where k is the capacity). For infinite capacity queues, it is 0. Override as needed.

Attributes

def a: Double

The overAll traffic intensity or rate ratio.

The overAll traffic intensity or rate ratio.

Attributes

def l_q: Double

Expected length/number in the sYstem, Service and Queue.

Expected length/number in the sYstem, Service and Queue.

Attributes

def l_s: Double
def report(): Unit

Report the results.

Report the results.

Attributes

def t_q: Double

Expected time in the sYstem, Service and Queue (computed using Little's Law).

Expected time in the sYstem, Service and Queue (computed using Little's Law).

Attributes

def t_s: Double
def t_y: Double
def view(): Unit

View/check intermediate results.

View/check intermediate results.

Attributes

def λe: Double

The effective arrival rate = λ (1 - π_k) that factors in turn aways. For infinite capacity queues, λe = λ.

The effective arrival rate = λ (1 - π_k) that factors in turn aways. For infinite capacity queues, λe = λ.

Attributes

def ρ: Double

The server utilization factor (overall arrival rate / total service rate). Also referred to as the traffic intensity per server ρ (rho) in [0, 1] where 0 => always idle, 1 => always busy.

The server utilization factor (overall arrival rate / total service rate). Also referred to as the traffic intensity per server ρ (rho) in [0, 1] where 0 => always idle, 1 => always busy.

Attributes

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