# Questions tagged [queuing-theory]

Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service.

35 questions
Filter by
Sorted by
Tagged with
51 views

### Confusion with Expected Queue Length (Lq) Formulas for M/M/s Model in Queuing theory

I have found two formulas for Expected Queue Length $L_q$ for the M/M/s model regarding Queuing Theory, namely: Found inside the "Introduction to the Operations Research" book made by ...
1 vote
35 views

### Queueing system with 2 heterogeneous servers with prioritizing customers

This is a special case of a $M/M/c$ queuing system with $c=2$. Here, there is a single customer queue that feeds into two servers, one of which has a higher rate of service than the other. Call them ...
63 views

### How does one model weather in Simio and have it change how vehicles operate within the model?

For context, I am using the Simio modeling software for an OR class, and for fun I am making a simulation model of the traffic outside my dorm. I have recreated the layout and distance of the streets, ...
1 vote
18 views

### Service probability for M/M/c queue for reneging where reneging time is a function of service time

There is an M/M/1 (getting a result for M/M/c is ideal) queue with arrival rate 𝜆 and service rate 𝜇 and participants can renege. However, the difference between normal reneging settings (constant ...
1 vote
23 views

### Understanding queueing theory used to model the vehicle routing problem

I am trying to understand some journal articles on the vehicle routing problem, specifically Vehicle routing with dynamic travel times: A queueing approach and An M/M/c queue model for vehicle routing ...
62 views

### Loan Allocation Problem

I need help with the following use case: Context : Let's say there is a fintech "F", that helps with aggregating personal loans. Now, "F" can pool in customers who need a personal ...
38 views

### m/m/1/k=1 variance

Is there a nice formula for the finite time variance of the m/m/1/k=1 queue in steady state? (Exponential arrivals $\lambda$, exponential service time $\mu$, 1 server and no queue, so if a job arrives ...
42 views

### Modeling an assembly line as a batch processing $M/D^{(b,b)}/r$ queue

Consider an assembly line where some parts are produced in a station following a Poisson process with a rate of $\lambda$. These parts are put directly in a bin (transfer time to the bin is negligible)... 1 vote
246 views

### The impact of utilization rate of a queueing system on its average queue time

For an $M/M/c$ queue where arrivals follow a Poisson distribution with rate $\lambda$ and are iid, service follows a Poisson process with rate $\mu$ and there are $c$ parallel servers, we can estimate ... 1 vote
84 views

135 views

### Model or State Uncertainty in Queueing Model due to uncertain arrival rate

Introduction I am currently modelling a scenario where two queues need to be served by a single server in a non preemptive discipline. I am quite sorted on generating the optimal policy via Value or ...
### Queuing models in R, $\lambda$ Little
It's noted that the number of folks in a stationary system will maintain an average equal to the rate of arrival multiplied by the mean of the service distribution. The formula $L = \lambda w$ is ...