Questions tagged [queueing]

The mathematical study of waiting lines.

33 questions with no upvoted or accepted answers
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299 views

Dynamics of birth-death process with discouraged arrivals (alternatively, M/M/1 queue with balking customers)

Take a continuous-time birth-death process, where $k \in \{0,1,\ldots\}$ is the count and the arrival rate of death is $\mu \geq 0$ for $k = 1, 2, \ldots$ the arrival rate of births is $\alpha_k > ...
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250 views

Probability of collisions in queues of Poisson process

I have a process whereby objects of width $W$ land on a gene at rate $F$ (per second, poisson process, lets assume), and then start to move along at constant speed $V$. I'm trying to work out the ...
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168 views

Continuous time Markov chain forward equation

This is a homework question and I need suggestion how to approach it. We have given the transitions $\ i\rightarrow i+1$ with rate $\lambda(i)$ where $\ i \ge 1$ $\ i\rightarrow i-1$ with rate $\...
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6 views

calculating variance in a queueing model which looping flow

For the verification of a Discrete Event Model of a queueing model that I programmed, I would like to calculate the steady state values of the queueing times at different stations and their variance ...
2
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0answers
37 views

Distribution of shifted and censored random variable

Suppose I have a non-negative random variable $X$ with finite mean $\mu$. Let's for example assume it denotes demand, and we denote by $X(t)$ demand in period $t$, demand in different periods are iid. ...
2
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0answers
18 views

optimal scheduling allocation between online and walk-in queues

I have a scheduling queue that can be split between walk-ins and online booking appointments. In order to serve these queues I have a limited number of resources available. What is the optimal way to ...
2
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1answer
328 views

Queuing Theory: Customers arrive at a fast-food restaurant at the rate of 120 customers per hour

During lunch hour, customers arrive at a fast-food restaurant at the rate of 120 customers per hour. The restaurant has one line, with three workers taking food orders at independent service stations. ...
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145 views

What is the average number of students waiting in line

For this Question, am having a problem determining the average number of students in the queue. My problem arises since by using the formula, am getting a decimal answer less than 1. The formula I ...
2
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0answers
578 views

How to visualise queue wait time

Suppose I have a process that works as follows: collect all outstanding requests process all of them, which takes time commit all results in one transaction repeat I get a data point (start, ...
2
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0answers
62 views

How to predict how long a worker will take to perform a task when performance on the task is only known for other workers?

I am trying to model a queue system (via simulation) to see if I can make different work assignments to improve the overall performance (based on a number of metrics). I have historical records of ...
2
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0answers
522 views

Queueing Theory: How to estimate steady-state queue length for single queue, N servers?

I have a real-life situation that can be solved using Queueing Theory. This should be easy for someone in the field. Any pointers would be appreciated. Scenario: There is a single Queue and N ...
1
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1answer
24 views

Birth Death process

An office has two employees that process incoming orders. these two are always busy and they process the orders at the rate of 100/day for each person. However they are smokers. On an average they ...
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28 views

Distribution of the idle time in a queue

I have iid random variables $D_t \sim \mathcal{N}(\mu, \sigma^2)$ and a constant $Q$. Define a random variable $Z_t = (Z_{t-1} + Q - D_t)^+$. Essentially $Z$ is the waiting time distribution in a ...
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28 views

Total hourly profit for a single-server food stand

Customers arrive to a single-server food stand according to a Poisson process with rate $20$ per hour. The time to serve a customer is exponentially distributed with a mean of $2$ minutes. (a) The ...
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110 views

Burke's Theorem for rejection from Erlang-B loss queue

I have some general uncertainties regarding the rejection process from an Erlang-B loss queue ($M/M/c/c$), where the total capacity of the queue is equal to the number $c$ of servers. Consider the ...
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34 views

Which methods do people use to understand queueing networks?

Queueing networks can be analyzed through analytic results (in some cases), approximation methods or simulation (discrete-event simulation, system dynamics). Analytic solutions do not exist in general....
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94 views

Revenue Forecasting using Markov Chain or Queuing Theory?

I am trying to forecast revenue for a HealthTech giant that sales HealthTech Hospital Equipment like Ultrasound, Magnetic resonance, CT AMI etc. The nature of business is Build to Order, which means ...
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0answers
34 views

State-dependent tandem network of queues

I've been studying network of queues and I would like to model a system by a tandem state-dependent network of queues. I know Jackson network works for $M/M/$ networks, but not for queues where the ...
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0answers
30 views

Treatment of waiting time data with repeated observations for a finite time

A call center is open for 9 hours every day. My data are the times of occurrence of calls, divided in days. Some days are busier than the others and some days no calls at all occur. I have to estimate ...
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0answers
39 views

Distribution of “priority” emails among agents with different speeds (strange question)

but I figure if someone knows how to answer it, it may be someone here. Basically I have this weird distribution where the customer service agent speed (in terms of contacts per hour) is very ...
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42 views

mean queue delay ( nonpreemtive priority)

I'm trying to solve a problem where all arriving items (arrival exponential $\lambda = 1/5$) are divided into into groups, those who are served within 5 units of time and those who have their service ...
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54 views

is this two dimensional markov chain correct for this queueing system?

the problem that i have two single server station with no queuing space a customer goes to station 1 if it is available else it goes to station 2 if it is available or it will be lost output from ...
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28 views

probabilities related to a transient single-server queue

Consider an $N = 1$ server queue with arrival rate $\lambda > 0$ and service rate $\mu = 1$. If the process is transient, find $\rho{_{x0}}$ for $x ≥ 1$. My attempt: The process is transient if $\...
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15 views

How to determine the rate of input in a queue M/M/c?

I know the exit rate ($\mu$) and the average waiting time in the queue ($W_q$). I need solve to rate of input ($\lambda$) in a queue. $\rho = \frac{\lambda}{c\mu} < 1$ $\pi_0 = \left[\left(\sum_{...
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38 views

simulation in R: reading arrival times and service times from a set and have priority queue

I want to simulate an outpatient clinic that does not have walk-in. based on a scheduling model, I have already calculated arrival times and examination times and whether the patient will be a show or ...
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37 views

Utilization vs Percentile

My objective is to have high utilization of the resources by keeping only the required number of resources alive. Low utilization means the resources were not used effectively, while high ...
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22 views

In queueing delay, why can there be $+1$ added?

Here in p.4. a typical treatment on computing of queue delay is given. However, I've seen the equation $$W_n=W_{n-1} + Y_{n-1} - X_n$$ where $W_n$ is queueing delay, $Y_n$ is the service time of $n$...
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76 views

Modeling worker performance parameters for optimum allocation of tasks to workers

Lets say we have an English to French translation task in a company and there are 100s of workers who are proficient in doing this task but each worker has its own unique attributes which allow them ...
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139 views

Model design for queue position prediction

The goal of the model is to predict progression in position in a FIFO queue, given our current position and other predictor variables. This is progression in the sense that the number ahead of us in ...
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1answer
182 views

Time series tracking queue optimization problem

In order to track prices of many different products from different sources, I must optimally schedule a group of trackers dedicated to price collection (ie. collect one price at a time for each ...
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86 views

MLE Estimator for a state transition problem

Suppose that people arrive at a location $l_1$ and move to a nearby location $l_2$ at various points in time. We are interested in modelling the transition from $l_1$ to $l_2$. We suspect that the ...
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282 views

How to find and describe regularities in a distribution of interarrival times of a recurring event?

I want to see if there are regularities in interarrival times of a recurring event in discrete time. I know that I can fit distributions to the interarrival time distribution, but are there other ...
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117 views

What is the average expectation value of two specific objects in a queue?

I need some hand to solve this problem. Suppose a queue can be filled by three type objects (M, F and A). Depending on the number of each objects the line length can be different. We are looking ...