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A search game on a finite and complete graph is studied between a (immobile) hider and a seeker. A strategy for the hider is to choose a node where he hides, except for a specified node. A strategy for the seeker is an ordering of nodes in which the seeker starts at the specified node, examines each node in that order until he finds the hider, traveling along edges. Associated with an examination of a node is the examination cost, and associated with a movement from a node to a node is a traveling cost. These costs are unknown for both players when they choose strategies. They know only probability laws of them. While the hider wishes to maximize the expectation of the sum of these costs which are required to find the hider, the seeker wishes to minimize it. The game is solved when the nodes are classified into two groups depending on the examination costs, and the edges are classified into three groups depending on both costs.

Both response time and processing time become recently big problems in the processing time of various online and batch systems. Especially, the access efficiency of the database should be greatly controlled as for the speed of the processing time of accesses to the database. Because records are inserted far from their logical position, the storages of deleted records occupy some diverse spaces in the database. Then, to cover the weak point of the database, we execute the database reorganization at suitable times to achieve a good performance requirement for the application. There are two types purposes of the database reorganization: The purpose of physical reorganization is to optimize the database storage and to improve the database structure. However, as the database has usually access locality, its data structure may deterirate in limited parts of the storage space. Thus, we adop the partial reorganization. This reorganizes only locally structurally deteriorated space in the database, while the structural efficiency can be recovered similarly to the full reorganization. This paper considers two structural deteriorations which increase with time and occur independently in time. When the amount of deterioration is estimated at periodic time and at a specified time, the expected cost rates are obtained, using the cumulative damage model, and optimal policies which minimize them are discussed and analytically. We compute optimal policies for two models and compare them numeically.

This paper proposes a replacement policy for a cumulative damage model where a unit suffers damage caused by both shocks and inspections, and fails when the total damage has exceeded a failure level. To detect such failure, a unit is inspected at periodic times kT(k = 1, 2, …), and is replaced by a new one at detection of failure or at time nT, whichever occurs first. The expected cost rate is derived, when shocks occur at a non-homogeneous Poisson process, and an optimal number n* which minimizes it is discussed. Numerical examples are finally given.