QUEUING THEORY Flashcards
Provides ways of assessing impacts of activities by knowing the magnitude of vehicular delay and extent of queue propagated
Queuing Analysis
Queuing Analysis: Provides ways of assessing impacts of activities by knowing the _______ of vehicular delay and _______ of queue propagated
Magnitude
Extent
Queuing Analysis models are derived on assumptions related to ___________ and prevailing __________
Arrival and Departure Patterns
Queue Discipline
A parameter that explains how the customers arrive at a service facility
Queue Discipline
Customers are served in the order of their arrival
First in First Out (FIFO)
Customers are served in reversed order of entry
First in Last Out (FILO)
Customers are selected for service at random irrespective of arrival in the service system
Served In Random Order (SIRO)
Customers are grouped in priority classes on the basis of some attributes (Service Time, Urgency, Identifiable Characteristics)
Priority Service
Server is switched between all queues for a predefined slice (quantum) of time in a round-robin manner
Processor (Time) Sharing
Each queue head is served for that specific time
Processor (Time) Sharing
Used to avoid server time killed by customer for external activities
Processor (Time) Sharing
Characterized by arrival patterns given by arrival distribution
Input
Depends on queue discipline and service mechanism at the service station
Output
Manner customers are served at the station
Service Mechanism
Popularly used to describe a queuing system
Kendall’s Notation
A/B/C (n)
Arrival and Departure Patterns follow
Markov (M) or Deterministic (D)
Random process or non-uniform distributions
Markov (M)
Processes characterized by regular or constant (uniform) arrivals or departure distribution
Deterministic (D)
Models of Traffic Distribution
Uniform Distribution (Deterministic)
Poisson Distribution (Non-Uniform)
Negative Exponential Distribution
Assumes all vehicles arrive equally or are uniformly spaced
Uniform Distribution (Deterministic)
Assumes that vehicles arrive at random
Possion Distribution (Non Uniform)
Assumption of Poisson vehicle arrivals also implies a distribution of tie intervals between arrivals of successive vehicles (time headway)
Negative Exponential Distribution
Regular arrivals and departures with single server; limit queue is at 100
D/D/1
Arrival and departure are easily represented by straight lines with slope corresponding to their rates (flow)
D/D/1
Assumes that arrivals follow a negative exponential distribution (random) and regular departures; has a single server
M/D/1
Traffic density of M/D/1
Rho = Lamda/Mu
Utilization factor of M/D/1
Rho = Lamda/Mu
Random arrival and departure (service rates)
M/M/1
Negative exponential distribution for both arrival and departure
M/M/1
Random arrival and departure/ Multiple Servers/
M/M/N
Traffic density of M/M/N
Rho = Lamda/Mu
Utilization factor of M/M/N
Rho/N
