Interest charges and likelihood of inventory overflow

Dmping time fromthe equations.

The agent is willing to purchase inventory on credit if the line is short. The effect is t transfer the risk of inventory overflow from the source to destination along a value chain. The likelihood count is taken over the total depreciation cycle of the finite chain. Each node in the chain engages in some fraction i of transactions total.  The distribution of inventory count is binomial in the number of items in inventory.  But at each level of the chain the sample rate decreases, going up. That is the equivalent of an unfair coin. it is (1/2)^-iLog(i), as that centers the binomial.

This case is a simple two color, the queue manager watches the costumer two times around the cycle and the supplier once. The queue manager know the total number of transactions, he has to pick i, the proper number of inventory items.

The currency banker is charging the insurance charges for items per basket not meeting -iLog(i). The charges applied upon disequilibrium.  And that is the theory of economics, we do not like waiting in line, especially us antificants.

N is a fuzzy constant, that is what triggers the whole 1,2,3, 3/2  problem in sequencing which Markov does not cover at any energy level.  Markov is a condition imposed on the node. But the additional burden means adding allowance to send the map, or always find the next best guess of N. There is a point in which some subset of the items will better estimate N.

The system is always slightly off equilibrium.  Consider the queues profit, sales, expenses and variance in N.  Walmart is not a proton, it has high variance in N. But they march up the *1,y,z) chain, keeping their fourth member, the queue manager, at a standard one and a half unit variance. They run a manipulated 4D system.  That is where they do time and price, anything before that is items per basket at scale, or agents do not like long lines.
Neat trick. The Walmart manger knows the regular variance count. So he takes the Markov triple and ads a relative prime, 3e, e being the variance count from N, a fuzzy constant.  Then constructs the 24D with known xyz, back computes e, an irrational.   But it tells the manager if he needs to sample the flow more or less often, it sets his items per basket, as the fourth element, pit boss.

Computing the map in dimension m+1 for dimension m. Great tool for financial analysis as Markov are really arrival rates, which is what the investors need. Pit boss risk is equivalent to likelihood to inventory failure in the chain. The investors can flatten that to linear time, get rates over time.

If the impl;ied number of items in the pit boss basekt jumps then the pit boss will redistribute the excess across the three relative arrival rates, find the next best spot on the 3 tuples.
The pit boss has a move pending. It updates the account and checks the implied sample rate against the contract.  The contract says the pit boss intervention rate is high and relatively prime, say 13.

The pit boss takes any surplus and supplies any deficit from he current scale.  When the imbalance in the pit boss account exceeds one. The contract specifies sample rates and Markov node.  The basic interest swap to keep contract is the risk of overflow over the whole cycle. The pit boss is moving the system from 3 to 4, the cost of the map.  Multiplying sample rates means adding in Bayesian space, so the implied fourth dimension is the uncertainty of kinetic energy, the sum is the fine structure, always 137. Walmarts goal is (3/2)^108.  Same as physicist.  Relative primes clime more steeply when dimension increases. One can see the Walmart fourth hand will have something like 29 eggs in the basket.  If you think of it as three queues, then the walmart manager circles the queue at least twice the rate of any arrivals, thus maintaining structured queues. each queue is the best estimate of a centered binomial producing i, items per basket, which becomes rate in sample space.

Short cuts.

Walmart has no control over customer arrivals, so the pit boss function is absorbed into supply. There are other methods of dimension reduction. In the sea of customers, N to more accurate N,  there is a poiny where the fourth rate takes no unusual actions and the four relative primes are found.