This is a simple simulation of a (public transit) rail station, with stored value media.  
A portion of the population has enough value on their cards to simply walk up to the gates and go.  Others will not, and have to use slower vending machines.  Based on the crowds, how many devices do you need?  Based on the population, what the ratio of devices you need?

Public Transit Rail Patron Flow

Refinery products can be shipped to various destinations using multiple modes of transport. For example, a refinery could be shipping to some depots through pipeline, some through rail and some through ships. Each of these modes of transport have a particular batch size and the arrival rates could vary. Meanwhile, the refinery could be producing MS/HSD at a particular rate (and std. dev). This model simulates the impact of the inflow and outflow on the storage capacities. The assumption is that if the mean flow on inbound is balanced with the total mean flow on outbound, the storage levels would fluctuate within certain bounds. Would they? We can simulate and see. This model requires validation with the field study as well.

Oil Petroleum Fuel Shipping Pipeline Rail Multimodal Equilibrium Chaos

This is a simple simulation of a (public transit) rail station, with stored value media.  
A portion of the population has enough value on their cards to simply walk up to the gates and go.  Others will not, and have to use slower vending machines.  Based on the crowds, how many devices do you need?  Based on the population, what the ratio of devices you need?
Note: this simulation refers to patrons 'needing to topup' reloadable tickets, but this could equally represent patrons purchasing one off, or multi-use tickets.

Public Transit Rail Patron Flow

This is a simple simulation of a (public transit) rail station, with stored value media.  
As trains enter the station groups of patron will attempt to exit the station at the same time. How long do patrons need to wait to exit the station? What impact would additional gates make to the wait time?

Public Transit Rail Patron Flow

Refinery products can be shipped to various destinations using multiple modes of transport. For example, a refinery could be shipping to some depots through pipeline, some through rail and some through ships. Each of these modes of transport have a particular batch size and the arrival rates could vary. Meanwhile, the refinery could be producing MS/HSD at a particular rate (and std. dev). This model simulates the impact of the inflow and outflow on the storage capacities. The assumption is that if the mean flow on inbound is balanced with the total mean flow on outbound, the storage levels would fluctuate within certain bounds. Would they? We can simulate and see. This model requires validation with the field study as well.

Oil Petroleum Fuel Shipping Pipeline Rail Multimodal Equilibrium Chaos