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Purpose – This chapter investigates fathers who have both biological and social children from different relationships in order to examine how they prioritize between their children, both in theory and in practice.

Methodology – Interviews were conducted with 57 low-income fathers in Oakland experiencing multiple-partner fertility.

Findings – These fathers used nine criteria to prioritize children: timing of life course interruptions, distance, formal child support, desirability of the pregnancy, restraining orders, other resources available to the child, age of the child, gender of the child, and the child's reaching-out behavior.

Research implications – These fathers distribute finite resources of time and money using priority-ordered queuing. This method allowed them to maximize their impact by focusing on a small number of children, rather than having their scarce resources become so diffuse that they became virtually meaningless.

Practical implications – These fathers utilized priority-ordered queuing, in contrast to the equal-distribution queuing method preferred by child support enforcement agencies. The difference in queuing model preference may explain fathers’ noncompliance with child support orders.

Value – In contrast with previous research findings, this chapter finds that these fathers were more likely to be simultaneously “good fathers” and “bad fathers” to different children at the same time, rather than one or the other (Furstenberg, 1988). This chapter also demonstrates a novel use of queuing theory for family research.

The duration of an urban search and rescue (USAR) operation directly depends on the number of rescue teams involved. The purpose of this paper is to simplify the earthquake environment and determine the initial number of rescuers in earthquake emergencies in USAR operation.

In the proposed methodology, four primary steps were considered: evaluation of buildings damage and the number of injured people by exerting geospatial information system (GIS) analyses; determining service time by means of task allocation; designing the simulation model (queuing theory); and calculation of survival rate and comparison with the time of rescue operations.

The calculation of buildings damage for an earthquake with 6.6 Richter in Tehran’s District One indicated that 18% of buildings are subjected to the high damage risk. The number of injured people calculated was 28,856. According to the calculated survival rate, rescue operations in the region must be completed within 22.33 h to save 75% of the casualties. Finally, the design of the queue model indicated that at least 2,300 rescue teams were required to provide the calculated survival rate.

The originality of this paper is an innovative approach for determining an appropriate number of rescue teams by considering the queuing theory. The results showed that the integration of GIS and the simulation of queuing theory could be a helpful tool in natural disaster management, especially in terms of rapid vulnerability assessment in urban districts, the adequacy and appropriateness of the emergency services.

The purpose of this paper is to focus on the contributions of queueing theory to hospital capacity management to improve organizational performance and deal with increased demand in the healthcare sector.

Models were applied to six months of inpatient records from a university hospital to determine operation measures such as utilization rate, waiting probability, estimated bed capacity, capacity simulations and demand behavior assessment.

Irrespective of the findings of the queueing model, the results showed that there is room for improvement in capacity management. Balancing admissions and the type of patient over the week represent a possible solution to optimize bed and nurse utilization. Patient mixing results in a highly sensitive delay rate due to length of stay (LOS) variability, with variations in both the utilization rate and the number of beds.

The outcomes suggest that operational managers should improve patient admission management, as well as reducing variability in LOS and in admissions during the week.

The queueing theory revealed a quantitative portrait of the day-by-day reality in a fast and flexible manner which is very convenient to the task of management.

The purpose of this paper is to investigate how queueing theory has been applied to derive results for a Sparre Andersen risk process for which the claim inter‐arrival distribution is hyper Erlang.

The paper exploits the duality results between the queueing theory and risk processes to derive explicit expressions for the ultimate ruin probability and moments of time to ruin in this renewal risk model.

This paper derives explicit expressions for the Laplace transforms of the idle/waiting time distribution in GI/HE_r(k_i,λ_i)/1 and its dual HE_r(k_i,λ_i)/G/1. As a consequence, an expression for the ultimate ruin probability is obtained in this model. The relationship between the time of ruin and busy period in M/G/1 queuing system is used to derive the expected time of ruin.

The study of renewal risk process is mostly concentrated on Erlang distributed inter‐claim times. But the Erlang distributions are not dense in the space of all probability distributions and therefore, the paper cannot approximate an arbitrary distribution function by an Erlang one. To overcome this difficulty, the paper uses the hyper Erlang distributions, which can be used to approximate the distribution of any non‐negative random variable.

This paper considers correction aspects of computer communication networks modelling with emphasis on their performance evaluation. In general, the problem is to achieve the highest possible performance given constraints on the system.

The paper reviews the application of the analytical methods, based on the queueing theory, to the computer communication systems and makes an extension of theory to the improvement of the developed analytical models. In this sense the paper describes the derivation of a correction factor for analytical models to study more precise their basic parameters (end‐to‐end delay, performance, etc.).

The contribution is in incorporating the derived correction factor to account for the real non‐exponential nature of the input to the transmission channels of computer communication systems. The produced results by corrected analytical model are compared with results previously reported in the literature to estimate the magnitude of improvement.

The improved analytical models were tested under various ranges of parameters, which influence the architecture of the computer communication networks and which are important for practical use.

The rapid rate of growth of computer‐based communication systems (e.g. distributed computer networks, mobile data networks) has resulted in a renewed and intensive interest in this area. Efficient design of their service facilities leads to the sharing of resources among users. Such public shared networks are largely oversubscribed by independent users, which make random demands on the network resources. The optimal resource allocation to satisfy such demands and the proper settlement of contention when demands exceed the capacity of the resources, constitute the problem of being able to understand and to predict system behaviour.

To behaviour analysis we can use both analytical and simulation methods. Modelling and simulation are methods, which are commonly used by performance analysts to represent constraints and optimise performance. Principally the application of analytical queuing theory results belongs to the preferred method in comparison to the simulation method, because of their ability to analyse also very large networks.

This paper aims to consider a single server queue with system disasters and impatience behavior are evident in our daily life. For this purpose, authors require to know the general behavior of these systems. Transient analysis shows for us how the system will operate up to some time instant t.

In this paper, authors consider a single server queue with system disaster and impatient behavior of customers in a multi-phase random environment, in which the system transits to a repair state after each system disaster. When the system is in a failure phase or going through a repair phase, the new arrivals would be impatient. In case the system is not repaired before the customer’s time expires, the customer would leave the queue and never return. Moreover, after repair, the system becomes ready for service in an operative phase with probability $q_{i} \ge 0.$. Using generating functions along with continued fractions and some properties of the confluent hypergeometric function, authors obtained on their own results.

Explicit expressions have been obtained for the time-dependent probabilities of the underlying queuing model. Also, time-dependent mean and variance of customers in the system are deduced.

The system authors are dealing with is somewhat complicated, there are some performance measures that cannot be achieved, but some of them have been obtained, such as the expectation and variance of the number of customers in the system.

Based on the obtained results, some numerical examples are some numerical examples are presented to illustrate the effect of various parameters on the behavior of the proposed system.

Authors’ studied transient analysis of a single server queue with system disaster and impatient customer system is suitable for behavior interpretation of many systems in our lives, such as telecommunication networks, inventory systems and impatient telephone switchboard customers, manufacturing system and service system.

To the best of the author’s/authors’ knowledge and according to the literature survey, in a multi-phase random environment, no previous published article is presented for transient analysis of a single server queue with system disaster and impatient customer behavior in a random environment.

It is analytically difficult to derive the probability distribution function of waiting (or delay) time at the second or third queue in series of tandem queues. This paper presents a method by which approximation is done through a quasi‐isomorphic system which resembles the second queue in respect of one output, viz delay time. Through extensive simulation experiments these isomorphs have been derived. The procedure of getting a simple system to represent a part of a complex system is practised in cybernetics; this approach appears to have potentiality in studying intractable problems in communications and industrial management.