A queueing problem with batch arrivals and correlated departures

Summary This paper considers the steady state behaviour of a queueing system in which (i) the input following the Hypergeometric Distribution is in batches of variable size (ii) queue discipline is first come first served it being assumed that the batches are preordered for service purposes and (ii) the service at two consecutive time marks is correlated. Probability generating functions for the various cases have been obtained and the mean queue lengths derived.     

Time dependent solution of a queueing problem with correlated batch arrivals and general service time distribution

This paper considers the transient behaviour of queueing problem in which (i) the arrivals occur in batches of variable size (ii) the arrival and no arrival of a batch at two consecutive transition marks are correlated (iii) the service time distribution for each, unit is general with probability density functionD(x). TheLaplace transform of various probability generating functions of queue length are obtained and some particular cases are derived therefrom.     

On the queueing problem of correlated arrivals with many servers in a finite waiting space

This paper provides an analysis of the steady state behaviour of a discrete time, first come first served limited space queueing problem with many serers. The arrival probabilities at two consecutive time-marks are correlated, whereas the departure probabilities, though depending on the queue length, are assumed to be statistically independent. Probability generating functions for the queue length for the various cases have also been listed. A few particular cases have also been derived. Mean queue lengths are also found out.     

A queueing problem with arrival and service in batches of variable size

This paper studies the transient behaviour of a single-channel queueing problem wherein (i) the input, following aPoisson distribution, is in batches of variable size (ii) the queue discipline is first-come-first-served; it being assumed that the batches are pre-ordered for service purposes (iii) the output, following a general distribution, is in batches of variable size. TheLaplace transform of the probability generating function of the waiting line size is obtained and the corresponding results are derived when the service time distribution is (i) hyper-exponential with m branches (ii) phase-type and (iii) exponential. Finally, some particular cases are discussed.     

A priority queueing system with service interruptions

This paper studies a queueing system in which a mechanical service channel serves the units one by one on a priority basis and is subject to occasional breakdowns. During the period for which the mechanical service channel remains under repairs, the service is provided to only the units of priority class by a manually operated service channel. L aplace transforms of the probability generating functions of the queue length have been obtained and the corresponding results for the steady state have been derived. Finally a particular case has been discussed.     

Queues with hyper-poisson arrivals and bulk exponential service

Summary In this paper the time-dependent solution of a queueing system is discussed under the conditions (i) the units arrive according to Hyper-Poisson distribution withl branches (ii) the queue-discipline is ‘first come first served’ (iii) the Service-time distribution is exponential with maximum capacity ofM units being served at one instant. Some results have been obtained when the waiting space is finite; in particular the probability for service to be idle has been obtained. Also for infinite queueing-space case, the expressions for the state probabilities and the mean queuelength under steady state conditions have been found.     

Queues with batch poisson arrivals and hyper-exponential service time distribution

Summary We consider in this paper the transient behaviour of the queuing system in which (i) the input, following a Poisson distribution, is in batches of variable numbers; (ii) queue discipline is ‘first come first served’, it being assumed that the batches are pre-ordered for service purposes; and (iii) service time distribution is hyper-exponential withn branches. The Laplace transform of the system size distribution is determined by applying the method of generating functions, introduced in queuing theory byBailey [1]. However, assuming steady state conditions to obtain, the problem is completely solved and it is shown that by suitably defining the traffic intensity factor,ϱ, the value,p ₀, of the probability of no delay, remains the same in this case of batch arrivals also as in the case of single arrivals. The Laplace transform of the waiting time distribution is also calculated in steady state case from which the mean waiting time may be calculated. Some of the known results are derived as particular cases.     

Queueing problems with arrivals in general stresm and phase type service

This paper deals with the steady state behaviour of a discrete time, single channel, first-come-first-served queueing problem wherein the service phases at two consecutive time-marks are correlated but the arrivals occur in General Stream. Probability Generating functions for the number of phases are obtained under two different models each with assumption that the service phases at two consecutive time marks are (i) correlated and (ii) uncorrelated. For each case the mean queue lengths when the number of phases demanded by an arriving unit is one, are derived. Some particular cases are discussed.     

Theory and numerical solution of a discrete queueing problem

Abstract  A queueing problem is considered with one server, independent discrete inter-arrival times, and independent discrete service times. The steady state distribution of the waiting time is approximated by means of the solution of certain linear equations and applying a generalization of the L in -B airstow method for finding quadratic factors of polynomials.     

No-envy,solidarity, and strategy-proofness in the queueing problem

Given a group of agents, the queueing problem is concerned with finding the order to serve agents and the monetary transfers they should receive. In this paper, we characterize interesting subfamilies of the VCG mechanisms by investigating the implications of either no-envy or solidarity requirements. First, we present a characterization of the strategy-proofand envy-freemechanisms. Next, we present characterizations of VCG mechanisms satisfying one of two different formulations of cost monotonicity or population monotonicity. Finally, we show that among the envy-free and strategy-proof mechanisms, the only ones that satisfy one of two formulations of cost monotonicity or population monotonicity are extensions of the pivotal or the reward-based pivotal mechanisms.     

Commuter arrivals and optimal service in mass transit: Does queuing behavior at transit stops matter?

This paper considers whether the optimal (second-best) mass-transit policy under a uniform-fare constraint is affected by passengers' queuing disciplines, by comparing the first-in-first-out (FIFO) and the random-access queuing. We analyze the problem by extending the model of mass-transit in Kraus and Yoshida (JUE(2002)) to the case of random-access queuing. The model involves the optimal number and capacity of trains as well as pricing. It is shown that, when the shadow value of a unit of waiting time exceeds that of a unit time of being late, the passengers' queuing discipline does not have any effect on the optimal (second-best) mass-transit policy including the number of trains and runs, scheduling, and pricing. If in turn, the shadow value of a unit of waiting time is smaller than that of being late, then aggregate travel costs are lower with random-access queuing than with FIFO, due to randomization of passengers' positions in a mass.     

Solution of a transient state,limited space queueing problem with arrival and departure rates depending on queue length

Summary This paper provides an analysis of a transient state, single channel, limited space queueing problem. The queue discipline is first come first served. The arrival and departure rates depend on queue length. Ample use of Generating Functions andLaplace transforms have been made. A few particular and important cases along with steady state solutions have also been derived.     

A simple proof of the optimality of the best N-policy in the M/G/l queueing control problem with removable server

Abstract  An M/G/l queueing system with removable server is considered. The following costs are incurred: a holding cost of h per unit time per customer in the system, a cost of r_l(r₂) per unit time when the service mechanism is on (off) and a fixed cost of K₁,(K₂ ,) for turning it on (off).
In this paper we shall give a very simple proof for the well known and intuitively obvious fact that the best N-policy is optimal for the average cost criterion among the class of all policies by first proving that the average cost formula of that policy and its relative cost function satisfy the optimality equation for the average cost criterion. The optimality of the best N-policy is then an immediate consequence.     

A generalized correlated binomial distribution with application in multiple testing problems

A typical microarray experiment often involves comparisons of hundreds or thousands of genes. Since a large number of genes are compared, simple use of a significance test without adjustment for multiple comparison artifacts could lead to a large chance of false positive findings. In this context, Tsai et al. (Biometrics 59:1071–1081, 2003) have presented a model that studies the overall error rate when testing multiple hypotheses. This model involves the distribution of the sum of non-independent Bernoulli trials and this distribution is approximated by using a beta-binomial structure. Instead of using a beta-binomial model, in this paper, we derive the exact distribution of the sum of non-independent and non-identically distributed Bernoulli random variables. The distribution obtained is used to compute the conditional false discovery rates and the results are compared to those obtained, in Table 3, by Tsai et al. (Biometrics 59:1071–1081, 2003).     

A free-rider problem with a free-riding principal

In a moral hazard problem caused purely by joint production and not by uncertainty, we examine the problem faced by a principal who actively participates in production along with a group of agents. We show that, when designing the optimal output sharing rule, the principal need not look for anything more complicated than the frequently observed simple linear or piecewise linear rules. We also confirm the presence of a friction between the principal’s residual claimant role and her incentive to free-ride in the production process that prohibits her from completely mitigating the moral hazard problem. This paper is from the first chapter of my Ph.D. dissertation at The University of British Columbia, Canada, 1993. I would like to thank my thesis supervisor John Weymark for his many helpful comments and suggestions. I have also benefitted from the comments of Charles Blackorby, David Donaldson, Mukesh Eswaran, Kenneth Hendricks, Ashok Kotwal and Guofu Tan. An anonymous referee and an associate editor provided helpful suggestion. I am also grateful for the hospitality of the Indian Statistical Institute, Delhi Centre, and the Centre for Development Economics, Delhi School of Economics, where parts of the paper were revised while I was a visitor. I am solely responsible for any remaining errors and omissions.     

A continuous location problem with different norms

This paper considers a set of problems of fixing the number and location of facilities to cover a given set of demand points, such that each demand point is served within a range of known distance standards, where each facility can be located on the entire plane and the distance can be either measured in rectilinear, Euclidean or Tchebycheff units. It is shown that an optimum solution can always be found on a small finite set of points. Thus the optimum itself can be found by either complete enumeration of these points or by zero one integer linear programming techniques. Furthermore, it is shown that the least and the largest number of facilities are required for the rectilinear and the Tchebycheff cases respectively.     

A conventional statistical problem with irregular minimax behavior

Summary The problem of testing the mean vector of the two dimensional circularly symmetrical normal distribution with unit variances, where the data consists of just one sample point inR ², is examined for stability of -maximin criteria. If the null hypothesisH ₀ is the one point set containing the origin and the alternative set equal to the whole ofR ²–H ₀, then the -maximin is not unique. If a zone of indifference _I containingH ₀ is introduced, then the problem of testingH ₀ againstR ² – _I can turn out to have a unique -maximin test. In the present paper we show a class of such _I for which this is the case. We show further that, given any -maximin test for testingH ₀ againstR ²–H ₀, there is a decreasing sequence of _I , with intersection equal toH ₀, for which the corresponding sequence of -maximin tests forH ₀ againstR ² – _I approaches a limit (in the usual weak star topology) which is not equivalent to .     

A facility location problem with clients' preference orderings

The Simple Plant Location Problem (SPLP) consists in identifying a pattern of facilities among a set of potential sites so that the sum of the costs for opening the facilities and for supplying a group of geographically dispersed clients therefrom is minimized. It is posited in this framework that the locator rules on the allocation of the clients to the facilities. When the clients are free to decide upon which facility they will attend, their choices do not necessarily match the most economical supply pattern from the point of view of the locator. We suppose here that each client has a preference ordering on the list of potential sites whereby he determines his allocation out of any set of open facilities. This preference ordering depends on characteristics of the client, of the sites, and of the trip between the client's location and the sites. Mathematically, we translate the orderings into a set of constraints to be appended to the SPLP. This new problem, termed SPLPO, has a wide range of applications as shown by a series of examples. We present an algorithm for solving the SPLPO and extensive computational experiments are reported.     

A framework for service enterprise workflow simulation with multi-agents cooperation

Process dynamic modelling for service business is the key technique for Service-Oriented information systems and service business management, and the workflow model of business processes is the core part of service systems. Service business workflow simulation is the prevalent approach to be used for analysis of service business process dynamically. Generic method for service business workflow simulation is based on the discrete event queuing theory, which is lack of flexibility and scalability. In this paper, we propose a service workflow-oriented framework for the process simulation of service businesses using multi-agent cooperation to address the above issues. Social rationality of agent is introduced into the proposed framework. Adopting rationality as one social factor for decision-making strategies, a flexible scheduling for activity instances has been implemented. A system prototype has been developed to validate the proposed simulation framework through a business case study.