On the market, a cow man sold

Recently faced with an interesting puzzle. Let me offer you to think about it. I'm not sure that this has happened somewhere before, therefore, if you see in it any known problem covered in the scientific literature, I would be grateful for the information provided. I managed to get some kind of computational solution, but you can’t call it graceful enough, and since the goal here is to motivate the reader to do an independent search, I will not publish it now.

So, the task is quite a life.

A certain man is engaged in the resale of cows: he buys them for a fixed small price of a rubles from the local population and tries to sell them at a premium to market visitors. Suppose, for simplicity, that buyers are divided into n classes according to their solvency, and that to any buyer who came up to the peasant from the k -th class, he sells any of his available cows at a premium x k-th rubles. We assume that the appearance of the buyer of each class is described by a Poisson process with a certain load parameter l k-characteristic of this class. If at the time of the appearance of a buyer, the Peasant has no cows, then the first one does not queue up, but is removed back home and does not return back. There simply would have been no task, if not for two plausible conditions:

1) Every cow bought by a Peasant from the population eats per unit of time for rubles, so it is not profitable to keep a large supply of cows;
2) A man can always send a request with a companion to the village to bring in more cows, but the fulfillment of this request, although free, takes T time;
3) In view of the reservations made, the Peasant may not sell the cow if he has few of them, and the chance to meet the richer client is large enough, or vice versa, to sell at a loss from the excess stock just to feed for nothing.
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What is the optimal long-term strategy for a Man with an almost infinite initial capital?

Remarks :
1) a request for replenishment of cows is like a phone call to a delivery service - you can call as often as you wish, as long as there is money for prepayment, while all applications will be executed independently of each other exactly T time after the prepayment;
2) there are considerations in favor of the fact that Muzhik's capital with reasonable strategies will be like a random walk on a straight line, then under optimality should be considered maximizing the relationship of waiting for a shift to the right for a long period of time to the magnitude of this gap, while altogether, decreases asymptotically according to exponential law on the value of the initial capital