# Questions tagged [queueing]

The mathematical study of waiting lines.

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11 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 ...
55 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. ...
23 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 ...
180 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 ...
628 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, ...
63 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 ...
525 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 ...
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### How to Solve an Arrival Rate for a given Latency Percentile?

I've been cranking on this for some time and think some help would be nice. Say I've got an M/M/1 queue, and while I can't change my service time distribution, I can certainly adjust my arrival rate. ...
28 views

### users and licences

I have the following question: Suppose I have a product with $U$ users and $S$ seats (licences). Where $S < U$. A user may only use the given product if there are seats available, and during the ...
39 views

### Birth and death process, and calculating waiting time using Little's law

Assume that an individual only has two possible states: susceptible (S) and infected (I). Further, assume that the individuals in the population are independent, and that for each susceptible ...
51 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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### 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 ...
128 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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### 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....
105 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 ...
35 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 ...
31 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 ...
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 ...
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 ...
63 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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### 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 ...
39 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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### 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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### 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 ...
150 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 ...
189 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 ...
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 ...