The -temporal arrangement of periodic market systems has been intensively studied by many geographers. Especially R. H. T. Smith and his collaborators have developed some hypotheses: the consumer hypothesis, the traveling trader hypothesis, and so on. These hypotheses have been constructed, however, without taking into account the -temporal arrangement processes, so that their hypothses have been stated separately or as contrary to each other.
In taking account of their hypotheses, both locality in space and inertia in time are important characteristics. First, establishment of markets and market day selection are decided by the local authority concerned; the whole -temporal arrangement of periodic market systems must be explained as the results of the accumulated decision-makings in each local area. Second, markets initially set have been maintained for a long term, so that they have some relative advantages compared to markets newly set: the decision-making of market day selection in a market newly set in a stage is dependent on the former -temporal arrangement. It is relevant to operate a step-by-step simulation to take account of locality and inertia in the -temporal arrangement processes.
This paper aims at proposing a unified simulation model of the -temporal arrangement of periodic market systems. The model consists of the next three processes: the process of market day selection, in that the market day of a specific periodic market is selected by the local authority concerned in a way that no two neighboring markets have the same market day, which is called the “simple avoidance rule” (A. Hay, 1977): the process of historical development of periodic market systems, in which a new market is arranged to be accommodated to the -temporal arrangement of markets already set, which is taken into consideration by using the step-by-step simulation; the random process that setting markets is a random spatial process, and the market day of a market newly set is selected by a random process which is restricted by the two processes stated above. The algorithm of the Simulation Model 1 is represented in Figure 3.
Simulation Model 1 was executed 100 times to examine the -temporal arrangement of periodic market systems with market data from South Ch'ungch'eong Province, Korea in 1925. A simulated pattern would be only a possible -temporal pattern because of the predomination of random processes. Figure 6 represents the most likely -temporal pattern which is simulated by Model 1. The -temporal pattern most similar to the real one, however, cannot be well specified by only the condition of the simple avoidance rule.
Thus, the condition of traversability of traveling traders is added to Simulation Model 1. Noteworthily the condition of traversability of traveling traders is a specific case of the simple avoidance rule. In Model 2, numbers of 5-step, 4-step and 3-step circuits extracted from each simulated -temporal pattern in Model 1 are calculated by using matrix algebra in graph theory. Then, the real -temporal pattern (Figure 5) is compared to the simulated pattern wherein the traversability of traveling traders is maximized (Figure 7). It turns out that the simulated -temporal pattern corresponds to the real one for 21 of all 76 markets, excluding 7 markets used in creating the model. Comparing Figure 7 to Figure 6 reveals that trader's convenience is well taken into consideration in the real periodic market systems. Furthermore, the simulated -temporal pattern provided by Model 2 proved to predict by far more market days than that based on the completely random process, that is, randomly set markets and random market day selection.

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