Queuing theory provides models for the analysis, management and control of service facilities where customers arrive and are serviced in a particular probability distribution.

In this work, the Poisson distribution is used to analyze a system of inactive strings as a queuing system in which both arrivals and service of inactive strings are assumed completely random, with average arrival rate =? and average service rate =µ.

The design of a queuing system to manage and control the inventory of inactive strings is optimal when a steady-state prevails. If the number c of service rigs is to be determined, the procedure starts with determining the smallest integer c such that the "rig utilization factor" ?= <1 and to study the resulting values of the corresponding "measures of effectiveness" until a specific measure (such as the "waiting time") is obtained that is acceptable to the Company.

The specific choice of the number c depends on what the Company considers as acceptable from an economic viewpoint of the number of inactive strings to be repaired and the time lost during repairs.

The numerical examples given in this work provide insight into the problem that may not be obvious intuitively.


Uncertainty is an important characteristic in many real-life settings. In an oil/gas field, for example, wells can run into circumstances that impede their performance. For instance, wells can fall victim of mechanical problems in their completion or to changes in the reservoir conditions that could lead to undesirable economics or unacceptable HSE state of affairs. In these settings, the exact times and magnitudes of the events cannot be predicted with certainty. Such events usually require corrective intervention measures. Today, it is not unusual to see a field with hundreds of wells where tens of them are problematic and require intervention to correct, restore or even improve their performance.

Since such intervention might require a workover rig, the cost of a workover operation could equal or even exceed the drilling cost of a new well. This requires the optimal allocation of scarce resources. Therefore, the need is recognized to establish a cost-effective (efficient) management and control of the inventory of problematic wells.

This paper treats the inventory of problematic wells as a stochastic system. We propose the Markovian birth-and-death stochastic process to model the inventory system of problematic wells. This stochastic method is used extensively in Operations Research to model queuing and inventory systems, machine and facility maintenance processes, bank services, health-care systems, and population dynamics (References 1–9).

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