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One of interesting subjects in Data Envelopment Analysis (DEA) is estimation of congestion of Decision Making Units (DMUs). Congestion is evidenced when decreases (increases) in some inputs re- sult in increases (decreases) in some outputs without worsening (im- proving) any other input/output. Most of the existing methods for measuring the congestion of DMUs utilize the traditional de nition of congestion and assume that inputs and outputs change with the same proportion. Therefore, the important question that arises is whether congestion will occur or not if the decision maker (DM) increases or de- creases the inputs dis-proportionally. This means that, the traditional de nition of congestion in DEA may be unable to measure the con- gestion of units with multiple inputs and outputs. This paper focuses on the directional congestion and proposes methods for recognizing the directional congestion using DEA models. To do this, we consider two di erent scenarios: (i) just the input direction is available. (ii) none of the input and output directions are available. For each scenario, we propose a method consists in systems of inequalities or linear pro- gramming problems for estimation of the directional congestion. The validity of the proposed methods are demonstrated utilizing two nu- merical examples.

In a network flow, transit time of an arc is the time span that a unit of flow takes to travel through this arc. In most real-world systems, such as road traffic, communication networks, pipeline systems, transit time of an arc is not constant and may take a value, randomly, from among several possible values. In such systems, reliability is the main concern. Given a demand d, time threshold T, and budget B, we define the reliability as the probability that d units of flow can be sent from the source to the sink under time horizon T and budget B. In this paper, we propose a simple algorithm to evaluate the reliability of networks in which the transition times are stochastic variable.

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