Modeling the academic publication pipeline.

Moss, Steven E. ; Zhang, Xiaolong ; Barth, Mike 等

ABSTRACT

In recent years, many academic institutions have implemented more stringent academic qualification standards by increasing research requirements for faculty. This paper analyzes the impact of changing research requirements in terms of faculty research output. We model the academic research pipeline including review and revision processes as a queue network and study the stationary behavior of the research pipeline. Both a theoretical model of the publication process and a simulation showing numerous combinations of submission strategies and publication requirements are presented. Within this framework, research requirements can be analyzed via probability constraints on the output process, and the research effort that satisfies this constraint is derived. We also study the transitional behavior of the publication queue to understand the convergence towards the stationary solution. Our analyses shows that submission requirements substantially exceed publication requirements if a faculty member is to maintain a required number of publications over any given time interval.

INTRODUCTION

The purpose of this research is to evaluate the pipeline for publications as a queueing model and to evaluate the probability of success for producing a given number of peer-reviewed journal articles over a fixed time interval. Publications are an important aspect of tenure, promotion, and salary decisions for business faculty. The Association to Advance Colleges and Schools of Business International (AACSB), the premier accrediting body for business schools, requires that colleges of business clearly delineate research and publication standards for faculty, including quality standards.

The AACSB standards place a particularly strong emphasis on peer-reviewed journal articles. Although the accreditation instructions specify a long list of intellectual contributions other than journal articles, the example summary table included in the accreditation standard 10 related to faculty intellectual contributions uses only two categories of intellectual contributions: (1) peer-reviewed journal articles, and (2) other intellectual contributions. Because of this (perhaps) over-reliance on peer-reviewed journal articles as the standard of measuring the research productivity of faculty, peer-reviewed journal articles are perceived to be the gold standard for business faculty.

The process of taking a research idea from concept to publication includes several stages and can encompass considerable delays independent of the time it takes to process through peer review (Clark et. al., 2000). Although an informal review may improve the potential for a positive publication decision (Brown, 2005), the additional delay may reduce the available time a new academic has to establish a publications record in anticipation of tenure and promotion review.

The standards for intellectual contributions differ from college to college but still generally apply a numerical standard (e.g., three peer-reviewed publications within five academic years) and often a quality standard (e.g., one A-level peer-reviewed journal article per year). The standards have been increasing over time in both quantity and quality of peer-reviewed journal articles (Starbuck, 2005). At the same time, the delay between submission and response by journals has doubled in some disciplines over the last several decades (Azar, 2006). Once a paper is finalized in a suitable form and format for a target publication, the submission process begins, and that process can entail considerable delay in and of itself. A study done by Mason, Steagall and Fabritius cited in Clark et. al. (2000) reported that the average delay between submission and printing to be 35 weeks, and they reported instances where there were delays of over a year. Ellison (2002b) reports that the number of revisions and the length of time to process an article in the top economics journals has increased and that the average waiting time for an acceptance has increased to 20-30 months.

The publications pipeline for business faculty at state and regional universities can be significantly different than for their top-level business school colleagues. Publications in the lesser known journals can still entail a long delay, and the quality level of these journals is harder to measure. Acceptance rates and average review times are reported in Cabell's Directories of Publishing Opportunities, and administrators regularly use those published numbers to evaluate the quality of journals. Many academics also use Cabell's published figures to determine where to submit articles. However, the information in these directories is self-reported by each journal, and there is no standardized methodology for reporting acceptance rates. A self-reported acceptance rate of 40 percent in one journal may actually be more restrictive than a 20 percent acceptance rate reported in another. Given these caveats, a sample drawn from the 2006-07 editions of Cabell's Directories for Accounting, Economics and Finance, Management, and Marketing showed that all four disciplines had a mean acceptance rate of 25 percent, with the most common self-reported value to be 21-30 percent.

The acceptance rate for publications and the average delay between submission and acceptance are critical considerations for business faculty working towards promotion and tenure. Newly minted faculty members are not as cognizant of the delays built into the process and may easily underestimate the amount of work that is required to achieve those standards. Also, as pointed out in Frey (2003), the pressure to publish can often lead faculty members to respond slavishly to the whims of outside reviewers rather than to pursue their own academic and intellectual standards.

The publication process can be thought of as a queueing system, with a submission rate of X (the number of publications that a faculty member must submit per year) and a service rate of Y (the rate at which the submissions move through the pipeline). This research explores the effect of changes in the required number of journal articles over a fixed time interval and the submission rate of the author on the probability of successful completion of tenure and promotion requirements for business school faculty. In the next section of this paper we will present a theoretical queueing model for the academic publication process, modeled as a steady-state process. The following section will present a simulation approach of the publication process assuming varying research requirements and research strategies. We will conclude with a discussion of the findings and the potential impact on faculty working towards tenure and promotion as well as tenured faculty members working to maintain their academic qualifications.

THE ACADEMIC RESEARCH PIPELINE AS QUEUEING NETWORK

For simplicity, we assume that a researcher can follow one of two submission strategies: (1) submission directly to a B-level journal or (2) submission directly to an A-level journal and then follow up with a submission to a B-level journal if the paper is rejected by the A-level journal. The first strategy is the shorter route because the article goes through the review process only once, but it will also have a smaller probability of acceptance for the same reason. Some researchers (e.g., Azar, 2006; Starbuck, 2005) have blamed the increasing number of "frivolous submissions" (i.e., submissions of lower-quality articles to the top journals in the field) on the slowdown in the overall peer review system. In our model, we are also assuming that authors follow an ethical approach and submit their research to the appropriate level of journal, rather than take the shotgun approach.

In our model, authors submit articles to either an A-tier or a B-tier journal, with the A-tier representing the top journals in a particular field. This two-tier publication system is described using a two-stage queueing network with feedback. The first stage of the network represents submitting an article to an A-tier journal for review, which may be accepted, rejected, or revised for resubmission. An accepted A-tier paper exits the publication system. A rejected A-tier article is resubmitted to a B-tier journal. A revised paper can be resubmitted as a new manuscript or undergo a second review. For simplicity, we lump multiple reviews and revisions that often occur in top-tier journals into one round as a second review. We make a simplifying assumption that all papers are accepted after a second review, reflecting the fact that the vast majority of papers that undergo multiple revisions are eventually accepted. The second stage of our queueing network represents the B-tier journals. In addition to the arrival from rejected A-tier papers, a B-tier journal also has its own independent stream of direct submissions. The B-tier reviewing process is similar to the A-tier one except that the rejected papers are assumed to exit the publication system. The arrival of articles at each tier of journal is assumed to be Poisson distributed. A reworked paper that failed to be accepted in either an A or B-tier journal is treated as a new submission in the queueing system.

Our simplified publication system represents a Jackson network with feedback (Jackson, 1957, 1963). The following schema, see figure 1, depicts the 2-stage publication queueing network modeled in this paper.

[FIGURE 1 OMITTED]

Nodes 1 and 3 represent the A and B journal first review process respectively. Nodes 2 and 4 represent their corresponding revision queues. Nodes 5 and 6 represent the second review process of each tier. By convention, node 0 represents the outside of the publication system. The independent arrival rate for each node is represented by [[gamma].sub.i], while the routing probabilities between two nodes, representing key journal review statistics, are denoted by [[gamma].sub.ij], and their interpretation is shown in table 1.

Certain combinations of routing probabilities must add up to one. These combinations are shown by the four equations in table 2.

Because feedback is involved, the stationary distributions of the research output streams represented by [[gamma].sub.10], [[gamma].sub.30], [[gamma].sub.50], and [[gamma].sub.60] depends on the total net mean flow rate into each node. Let [[lambda].sub.i] be the total net mean flow rate into node i including the independent arrival from the outside and the feed back from other nodes. When the queue network converges to stationary equilibrium, the total expected inflow of articles must equal to the total expected outflow for each node. This balance of flow implies that the following equation must hold (Gross and Harris, 1985).

[[lambda].sub.i] = [[gamma].sub.i] + [[summation].sup.6.sub.(j=1)] [[gamma].sub.ji] [[lambda].sub.j]

Expanding the flow of balance equations for each of the six nodes in our publication network yields the six linear equations, shown in table 3.

The first equation simply states that the total net inflow into node 1 is the sum of the independent arrival and the feedback flow from node 2. The second equation indicates that the arrival to node 2 is a fraction of the outflow of node 1 according to our network structure. Other equations can be interpreted similarly. The overall mean arrival flow rates for each node can then be easily solved from the linear system of equations shown in table 3, which are given by the following six equations shown in table 4.

Given the overall arrival flow rates, the accepted article output streams associated with the A-tier and B-tier journals are independent Poisson processes with rates shown in table 5 (Melamed, 1979; Burke, 1956; Disney et. al., 1980).

Let [X.sub.A](t) be the number of A-tier journal articles accepted in a year, [X.sub.B](t) be the number of B-tier journal articles accepted in year t. Variables [X.sub.A] and [X.sub.B] are Poisson distributed due to the fact that they are sums of independent Poisson distributions. Therefore the sum of [X.sub.A] and [X.sub.B] is also Poisson distributed with mean rates shown below.

Rate = [[gamma].sub.10] [[lambda].sub.1] + [[gamma].sub.30] [[lambda].sub.3] + [[lambda].sub.5] + [[lambda].sub.6].

Let n be the number of articles needed in a m-year period to attain or maintain an Academic Qualification (AQ), be it tenure, promotion, or any other standard. Therefore probability of publishing the n articles can be calculated from the following equation.

P(AQ) = P([[summation].sup.m.sub.(t=1)] [X.sub.A](t) + [[summation].sup.m.sub.(t=1) [X.sub.B](t) [greater than or equal to] n)

where [summation][X.sub.A](t) + [summation][X.sub.B](t) is Poisson distributed with mean rate of m([[gamma].sub.10] [[lambda].sub.1] + [[gamma].sub.30] [[lambda].sub.3] + [[lambda].sub.5] + [[lambda].sub.6]).

Researchers can decide on a level of research effort measured by submission rates of [[gamma].sub.1] to A-level journals and [[gamma].sub.3] to B-level journals in order to achieve a desired level of probability in securing n journal articles and thus meeting their AQ status requirement. For example, if a researcher were to submit one ([[gamma].sub.1] = 1) A-tier paper and three ([[gamma].sub.3] = 3) B-tier papers a year and the statistics on journal acceptance, revision, and rejection rates were assumed to be as shown in table 6.

Substituting these input parameters into formulas for calculating the overall arrival rates at each node, shown in table 4, we can obtain the node arrival rate estimates shown in table 7.

Therefore, the annual research output would be Poisson distributed with a mean rate of 2.08. Derived as follows,

Mean rate = ([[gamma].sub.10] [[lambda].sub.1] + [[gamma].sub.30] [[lambda].sub.3] + [[lambda].sub.5] + [[lambda].sub.6])

2.08 = .05*1.06 + .1*3.85 + .26 + 1.38

If five published papers in five years are required to maintain academically qualified status, and the faculty member wishes to be 98% confident of achieving academically qualified status, our model shows that one A-tier and three B-tier submissions per year would be required.

Using the revision and rejection rates given in Table 6 as a baseline scenario, we calculate in Table 8 the overall mean research output rate and the probability of AQ when we vary the annual submission rates for the A-tier and B-tier journals.

The shaded cells in the probability table represent research efforts that produce better than 75% level of certainty in achieving AQ. Results in Table 8 suggest two strategies on allocating research efforts. First, if one wants to submit journals to only one tier (looking at the first row or the first column), one is better off in the long term to target the A-tier journals. The same number of A-tier papers achieves a higher average output rate than the B-tier papers, albeit over a longer period of time, since they have two shots at acceptance. Some academic researchers (e.g., Clark et. al., 2000; Ellison, 2002a, 2002b) have blamed this shotgun approach for the perceived backlog in the current review pipeline at the top tier journals.

The model shows that following the strategy of first submitting to an A-tier journal, with the rejected paper subsequently submitted to a B-tier journal, may result in a paper taking twice as long to work through the pipeline. However, this strategy may increase the overall acceptance rate for the author. This particular model looks at a steady state, and therefore it doesn't matter whether a paper takes one year or two years to go through the process because once it is in steady state, papers enter the pipeline and exit the pipeline at the same rate. Therefore, the adage of writing good papers and aiming high seems to be supported by our model.

To achieve a 75% chance of AQ with this focused strategy, one needs to submit 2 A-tier papers or 3 B-tier papers a year, a research effort two or three times higher than the required AQ output rate (one paper a year). Second, one can mix up the research effort and submit to both A-tier and B-tier journals. Again, A-tier articles are favored. For a fixed number of total mean submissions, for example four papers in a year, more A-tier articles increase the output rate and the probability of AQ.

We constructed two different scenarios to compare with the baseline case reported in Table 8. Table 9 presents the same results when the AQ requirement is doubled to ten papers in five years and Table 10 summarizes the case in which the acceptance rates for the A-tier and B-tier papers are doubled from the baseline level.

Changing the AQ standard has a significant impact on the research effort required to achieve AQ status with a desired level of certainty. Table 9 shows that if a 75% level of certainty of maintaining AQ is desired, then one needs to submit at least five papers in total if A-tier submissions are less than 3. If one submits three A-tier papers or more, one needs submit one less in total. Table 10 suggests that targeting journals with higher acceptance rates has much less effect on research effort than change AQ standards.

The stationary analysis seems to indicate that changing AQ standards can have a drastic impact on faculty's research effort in the long run. As an alternative, submitting to journals with higher acceptance rate will not likely offset this additional workload. The inherent uncertainty in the publishing process requires research efforts measured in number of annual submissions several times that of required by AQ standards in order to maintain a desired level of certainty for AQ. Academic administrators need to be aware of the resource implications when making changes to the existing AQ standards.

SIMULATING THE ACADEMIC RESEARCH PIPELINE

The model produced in the prior section is a steady state model, but the steady state may take years to achieve. Research (e.g., Clark et. al., 2000; Ellison, 2002b) shows that the review time for article submissions has been increasing over the past twenty years and is often measured in terms of years rather than months. The longer the turnaround time between submission and acceptance, the longer the time needed to reach steady state, all else held constant. However, in addition to the increasing time delay, the acceptance rate for the top journals in the major fields of business academics are decreasing (Swanson, 2004), making it even harder to meet the publications standards for tenure, promotion and merit pay increases imposed by colleges of business. Interestingly, as it becomes more difficult for newer doctoral faculty to publish in these academic journals, they are being evaluated by senior faculty and administrators who came up through a system with looser standards. The reality faced by newly hired faculty may differ from the perceptions of their older, more established colleagues, who may underestimate the existent limitations of today's research pipeline. The length of the review process and the rate of acceptance are therefore relevant concerns for faculty who are still in the process of reaching that steady state level of research productivity.

To assess various combinations of publication requirements and journal submission strategies a simulation model of the publication process is developed. In the simulation there are two decision variables, length of time between each new submission and the required number of publications over any given five years. Each submitted article in the simulation flows through a process. The first step is an A-tier journal review. For this review we use a Binomial distribution with a 5% acceptance probability. The journal review time is assumed to be Poisson distributed with a mean service time of 6 months. If the journal article is accepted it moves on to printing. The printing process is assumed to be Poisson distributed with a mean service time of 6 months from journal article acceptance, with a minimum time of 2 months. If the submitted article is not accepted we assume there is a 30% probability that the submission will receive a please revise and re-submit from the A-tier journal (Binomial 30%). The second review time is assumed to be Poisson distributed with a mean of 4 months. The combination yields an overall acceptance rate of 33.5% for A-tier journals.

In terms of this research these are more conservative estimates of acceptance rates and turnaround times than prior findings from Moyer and Crockett (1976) or Coe and Weinstock (1984) , but may be overly optimistic for some of today's A-level journals. The acceptance rate at the A-level journals is also affected by the number of frivolous submissions by authors hoping to slip an article through. If authors are submitting a large number of lower-quality articles so as to clog up the pipeline, the acceptance rates would be lower and the turnaround times would be longer. While there has been some limited research on the average acceptance rates and average turnaround times, there is relatively little on the variability of these values from one journal to the next. These parameters could also differ significantly from discipline to discipline (Swanson, 2004), so the choice of appropriate acceptance rate and turnaround time parameters is based partly on empirical evidence and partly on judgment.. Once the article is re-submitted we assume it is accepted after a second review time that is assumed to be Poisson distributed with a mean service time of 4 months. The accepted journal article then moves into the printing queue.

Articles not accepted in the A-tier journals are subsequently submitted to a B-tier journal. The B-tier simulation is identical to the A-tier process with the following changes to acceptance probabilities and service times. In the B-tier we assume there is a 10% probability of acceptance in the first review with a mean service time of 4 months. Rejected articles are assumed to have a revise and re-submit probability of 40%. This combination yields an overall acceptance rate of 46% for B-tier journals. The overall mean acceptance rate in the simulation for journal articles after submission to both A and B-tier journals with revise and re-submissions is 64%.

The month of printing is recorded for each accepted journal article. At the end of years five through eight a determination is made if the required number of journal articles has been printed over the prior five years. The process is simulated 1000 times and the percentage of time the required number of journal articles is achieved at the end of years five through eight is the simulation output.

The required number of journal articles over a specific period of time will, of course, depend largely on the goal of the researcher. The long-term rule of thumb for AACSB purposes has been two articles in the prior five years. Some schools have increased that level to three over the past five years, and generally speaking, the achievement of tenure would require even more. With respect to merit pay, some schools are quite competitive and faculty may be required to achieve multiple "hits" each year to maintain their equilibrium. The important point is that the requirements differ from school to school, and often include both a quantity requirements and a quality requirement. Therefore, the results shown here are meant more to illustrate how the probabilities of achieving success, differ based on the publications strategy.

SIMULATION RESULTS

Tables 11 through 14 show the probabilities that a required number of journal articles, one through five, will have been published for the prior 5 years given journal submission intervals ranging from six to eighteen months. The results are shown for the time periods ending year five through eight. For tenured faculty with an ongoing publication stream the later tables when the simulation has reached a steady state are more applicable. For new faculty with nothing in the pipeline facing tenure and promotion reviews the earlier tables may be more of interest.

For a tenured faculty member attempting to have a 90% chance of publishing 3 journal articles over any given five year period the results show they would need to submit an article every 9 months or submit 6.67 articles each five year period. If the publication requirement is reduced to 2 journal articles over five-years the required interval between submissions is approximately 13 months or submitting 4.6 articles each five-year period. Increasing the requirement to 4 journal articles increases the submission rate to one article every 7 months or 8.6 articles each 5-year period. Not shown is the required submission interval to be 90% sure of having 1 journal article in any given five year period. The submission interval is 24 months.

For new faculty with no papers in the pipeline the results show a higher required submission rate if the faculty member is to have the required number of articles in print by a the end of year 5 or 6. To have four articles in print would require submitting journal articles at rates in excess of 2 per year.

The simulation does not capture the possibility of varying an individual submission strategy based on prior successes or failures. The results are obviously sensitive to the assumed acceptance rates and review times. We feel the results are applicable when discussing a group of faculty and what will be required on average. More importantly the results clearly show the relationship between journal submissions and required articles is not one to one. The difference between required submissions and required journal articles is attributable to variation in review and printing times and acceptance rates below 100%. It should be noted that even if an author has a 100% acceptance rate, the variation in review and printing times will increase the required submission rate above the required publication rate if the author wishes to be confident that in any given 5 year period selected they will have the required number of publications.

CONCLUSIONS

The publishing pipeline is an important area of research for a number of reasons. First and foremost, faculty research expectations are an important aspect of the university teaching profession. This pipeline process has major implications for a faculty member's ability to attain tenure, promotion or pay raises. The increasing length of time in the review process and the increased stringency of the reviews are raising the standards independent of any increases imposed by university administrators. Simply put, achieving five publications in five years is harder to achieve today than it was ten years ago, and will be yet harder to achieve five years from now.

Our queueing network model stripped away some of the complexities associated with the academic publishing process. Our assumption of a two-tier system is not restrictive, however, because additional tiers can be appended to the B-tier and decomposed in a way similar to how we decomposed A-tier and B-tier. In our model, we only allow for one-round of revision. Multiple revisions can be easily incorporated by lumping them. Our results still apply if durations of multiple revisions are Poisson.

One limitation of our model is the assumption of self-serving queue. As a direction of future research, our model can be extended to consider the finite service capacity of a journal. This will allow us to analyze the impact of review time and the size of editorial staff on the stationary distribution of publications. Another limitation is our assumptions about acceptance rates and turnaround times. Published research shows that the acceptance rates and the turnaround times are changing over time and it is becoming more arduous to achieve success, especially in the top-level journals. Although acceptance rates are reported in Cabell's and are included in some of the journals, these acceptance rates are not necessarily comparable because they are not standardized. The information in Cabell's on both acceptance rates and turnaround times are self-reported by the various journals, and there is no real audit mechanism in place to check these numbers. An interesting line of research might be a study that verifies these values on a standardized basis, but we leave that to other researchers. Our simplifying assumptions about the acceptance rates and the length of the review cycle are agreeably subject to debate.

The surprising aspect of the publishing pipeline delay problem is not that it exists, but that so little research has gone into it. That is not to say that there is not published research in this field, but rather that there is relatively less than one would expect, given the importance of a research record on a faculty members success. This paper takes a step in that direction.

REFERENCES

AACSB (2006). Eligibility Procedures and Accreditation Standards for Business Accreditation, revised January 1, 2006.

Azar, O. (2006). The Academic Review Process: How Can We Make It More Efficient?, American Economist, 50(1), 37-50.

Brown, L. D. (2005). The Importance of Circulating and Presenting Manuscripts: Evidence from the Accounting Literature. The Accounting Review, 80(1), 55-83.

Burke, P. J. (1956). The Output of a Queueing System. Operations Research, 4, 699-714.

Cabells (2006). Cabell's Directories of Publishing Opportunities, found at ="http://www.cabells.com/" MACROBUTTON HtmlResAnchor http://www.cabells.com, accessed 8/15/2006.

Clark, A., J. Singleton-Jackson, and R. Newsom (2000). Journal Editing: Managing the Peer Review Process for Timely Publication of Articles. Publishing Research Quarterly, 16(3), 62-71.

Coe, R. & I. Weinstock (1984). Evaluating the Management Journals: A Second Look. Academy of Management Journal, 27(3), 660-666.

Disney, R. L., D. C. McNickle & B. Simon (1980). The M/G/1 Queue with Instantaneous Bernoulli Feedback, Naval Research Logistics Quarterly, (27), 635-644.

Ellison, G. (2002a). The Slowdown of the Economics Publishing Process. The Journal of Political Economy, 110(5), 947-993.

Ellison, G. (2002b). Evolving Standards for Academic Publishing: A q-r Theory. The Journal of Political Economy, 110(5), 994-1034.

Frey, B. S. (2003). Publishing as Prostitution? Choosing Between One's Own Ideas and Academic Success. Public Choice, 116(1-2), 205-223.

Gross, D. & C. W. Harris (1985). Fundamentals of Queueing Theory, 2nd ed., New York: Wiley Series in Probability and Mathematical Statistics.

Jackson, J. R. (1957). Networks of Waiting Lines. Operations Research, (5), 518-521.

Jackson, J. R. (1963). Jobshop-like Queueing Systems. Management Science, (10), 131-142.

Melamed, B. (1979). Characterization of Poisson Traffic Streams in Jackson Queueing Networks. Advances in Applied Probability, (11), 422-438.

Moyer, C. R. & J. H. Crockett (1976). Academic Journals: Policies, Trends and Issues. Academy of Management Journal, 19, 489-495.

Starbuck, W. H. (2005). How Much Better Are The Most Prestigious Journals? The Statistics of Academic Publication. Organization Science, 16(2), 180-202.

Swanson, E. P. (2004). Publishing in the Majors: A Comparison of Accounting, Finance, Management, and Marketing. Contemporary Accounting Research, 24(1), 223-253.

Steven E. Moss, Georgia Southern University

Xiaolong Zhang, Georgia Southern University

Mike Barth, Georgia Southern University

Table 1: Arrival Rates and Routing Probabilities

Var. Definition

[[gamma].sub.1]: A-tier journal submission rate

[[gamma].sub.3]: B-tier journal submission rate

[[gamma].sub.10]: Acceptance rate of A-tier journal

[[gamma].sub.30]: Acceptance rate of B-tier journal

[[gamma].sub.13]: Rejection rate of A-tier journal

[[gamma].sub.21] Percentage of revised A-tier articles resubmitted
 as new article to another A-tier journal

[[gamma].sub.25] Percentage of revised articles gone through
 a second review

[[gamma].sub.30] Rejection rate of B-tier journal

[[gamma].sub.34] Percentage of B-tier journals asked for a revision

[[gamma].sub.43] Percentage of revised B-tier articles resubmitted
 as new articles to another B-tier journal

[[gamma].sub.25] Percentage of revised B-tier articles gone
 through a second review

Table 2: Equations Constrained to 1

[[gamma].sub.10] + [[gamma].sub.12] + [[gamma].sub.13] = 1

[[gamma].sub.21] + [[gamma].sub.25] = 1

[[gamma].sub.30] +[[gamma]'.sub.30] [[gamma].sub.34] = 1

[[gamma].sub.43] + [[gamma].sub.46] = 1

Table 3: Linear Equations for Flow of Balance, Nodes One through Six

[[lambda].sub.1] = [[gamma].sub.1] + [[gamma].sub.21] [[lambda].sub.2]

[[lambda].sub.2] = [[gamma].sub.12] [[lambda].sub.1]

[[lambda].sub.3] = [[gamma].sub.3] + [[gamma].sub.13]
[[lambda].sub.1] + [[gamma].sub.43] [[lambda].sub.4]

[[lambda].sub.4] = [[gamma].sub.34] [[lambda].sub.3]

[[lambda].sub.5] = [[gamma].sub.25] [[lambda].sub.2]

[[lambda].sub.6] = [[gamma].sub.46] [[lambda].sub.4]

Table 4: Overall Mean Arrival Flow Rate for Nodes One through Six

[[lambda].sub.1] = [[gamma].sub.1]/(1 - [[gamma].sub.12]
[[gamma].sub.21])

[[lambda].sub.2] = [[gamma].sub.12] [[lambda].sub.1]

[[lambda].sub.3] = ([[gamma].sub.3] + [[lambda].sub.13]
[[lambda].sub.1])/(1- [[lambda].sub.34] [[gamma].sub.43])

[[lambda].sub.4] = [[gamma].sub.34] [[lambda].sub.3]

[[lambda].sub.5] = [[gamma].sub.25] [[lambda].sub.2]

[[lambda].sub.6] = [[gamma].sub.46] [[lambda].sub.4]

Table 5: Accepted Article Output Streams

 A-tier B-tier

Accepted in 1st review [[gamma].sub.10] [[gamma].sub.30]
 [[lambda].sub.1] [[lambda].sub.3]

Accepted in 2nd review [[gamma].sub.50] [[gamma].sub.60]
 [[lambda].sub.5] [[lambda].sub.6]

Where,

[[gamma].sub.50] and [[gamma].sub.60] = 100% by assumption

Table 6: Revision and Rejection Rates given 1 A-tier
and 2 B-tier Articles submitted per year

 A-tier B-tier

Acceptance [[gamma].sub.10] = 0.05 [[gamma].sub.30] = 0.1
Rejection [[gamma].sub.13] = 0.65 [[gamma].sub.30] = 0.5
Revision rate [[gamma].sub.12] = 0.3 [[gamma].sub.34] = 0.4
Resubmit as new [[gamma].sub.21] = 0.2 [[gamma].sub.43] = 0.1
Resubmit for 2nd
 review [[gamma].sub.25] = 0.8 [[gamma].sub.46] = 0.9

Table 7: Arrival Rates

 Node Arrival rate

[[lambda].sub.1] 1.06

[[lambda].sub.3] 3.85

[[lambda].sub.5] 0.26

[[lambda].sub.6] 1.38

Table 8: Sensitivity Analysis of Research Effort--Baseline

Annual Mean Rate of Research Output

 A-Tier Journal Submission Rate

B-Tier Journal 0 1 2 3 4 5
Submission Rate

 0 0.00 0.64 1.28 1.92 2.56 3.20
 1 0.48 1.12 1.76 2.40 3.04 3.68
 2 0.96 1.60 2.24 2.88 3.52 4.16
 3 1.44 2.08 2.72 3.36 4.00 4.64
 4 1.92 2.56 3.20 3.84 4.48 5.12
 5 2.40 3.04 3.68 4.32 4.96 5.60

Probability of AQ

 A-Tier Journal Submission Rate

B-Tier Journal 0 1 2 3 4 5
Submission Rate

 0 0.00 0.22 0.76 0.96 1.00 1.00
 1 0.10 0.66 0.94 0.99 1.00 1.00
 2 0.52 0.90 0.99 1.00 1.00 1.00
 3 0.84 0.98 1.00 1.00 1.00 1.00
 4 0.96 1.00 1.00 1.00 1.00 1.00
 5 0.99 1.00 1.00 1.00 1.00 1.00

Table 9: Sensitivity Analysis of Research Effort--Higher AQ Standards

Annual Mean Rate of Research Output

 A-Tier Journal Submission Rate

B-Tier Journal 0 1 2 3 4 5
Submission Rate

 0 0.00 0.64 1.28 1.92 2.56 3.20
 1 0.48 1.12 1.76 2.40 3.04 3.68
 2 0.96 1.60 2.24 2.88 3.52 4.16
 3 1.44 2.08 2.72 3.36 4.00 4.64
 4 1.92 2.56 3.20 3.84 4.48 5.12
 5 2.40 3.04 3.68 4.32 4.96 5.60

Probability of AQ

 A-Tier Journal Submission Rate

B-Tier Journal 0 1 2 3 4 5
Submission Rate

 0 0.00 0.00 0.11 0.49 0.82 0.96
 1 0.00 0.06 0.39 0.76 0.94 0.99
 2 0.02 0.28 0.68 0.91 0.98 1.00
 3 0.19 0.59 0.87 0.97 0.99 1.00
 4 0.49 0.82 0.96 0.99 1.00 1.00
 5 0.76 0.94 0.99 1.00 1.00 1.00

Table 10: Sensitivity Analysis of Research Effort--Higher
Acceptance Rate Annual Mean Rate of Research Output

 A-Tier Journal Submission Rate

B-Tier Journal 0 1 2 3 4 5
Submission Rate

 0 0.00 0.73 1.47 2.20 2.94 3.67
 1 0.58 1.32 2.05 2.79 3.52 4.25
 2 1.17 1.90 2.63 3.37 4.10 4.84
 3 1.75 2.48 3.22 3.95 4.69 5.42
 4 2.33 3.07 3.80 4.54 5.27 6.00
 5 2.92 3.65 4.38 5.12 5.85 6.59

Probability of AQ

 A-Tier Journal Submission Rate

B-Tier Journal 0 1 2 3 4 5
Submission Rate

 0 0.00 0.31 0.86 0.99 1.00 1.00
 1 0.17 0.79 0.98 1.00 1.00 1.00
 2 0.69 0.96 1.00 1.00 1.00 1.00
 3 0.94 0.99 1.00 1.00 1.00 1.00
 4 0.99 1.00 1.00 1.00 1.00 1.00
 5 1.00 1.00 1.00 1.00 1.00 1.00

Table 11: Probability of achieving required number
of journal articles at the end of year 5

Submission
 Interval Required journal articles

 (months) 1 2 3 4 5

 6 1.00 0.99 0.93 0.78 0.50
 7 1.00 0.97 0.87 0.59 0.30
 8 1.00 0.95 0.77 0.49 0.17
 9 1.00 0.91 0.71 0.33 0.08
 10 0.98 0.88 0.59 0.24 0.04
 11 0.98 0.82 0.52 0.13 0.01
 12 0.98 0.81 0.42 0.09 --
 13 0.97 0.76 0.34 0.06 --
 14 0.96 0.74 0.28 0.01 --
 15 0.94 0.65 0.23 -- --
 16 0.93 0.61 0.21 -- --
 17 0.91 0.56 0.13 -- --
 18 0.91 0.53 0.11 -- --

Table 12: Probability of achieving required number
of journal articles at the end of year 6

Submission Required journal articles
 Interval

 (months) 1 2 3 4 5

 6 1.00 1.00 0.98 0.92 0.77
 7 1.00 0.99 0.96 0.84 0.59
 8 1.00 0.98 0.92 0.75 0.45
 9 1.00 0.98 0.86 0.65 0.28
 10 1.00 0.96 0.80 0.50 0.18
 11 0.99 0.93 0.73 0.38 0.11
 12 0.99 0.91 0.65 0.32 0.07
 13 0.98 0.87 0.56 0.21 0.03
 14 0.98 0.84 0.52 0.17 0.00
 15 0.98 0.82 0.45 0.12 --
 16 0.97 0.79 0.39 0.08 --
 17 0.97 0.76 0.28 0.03 --
 18 0.96 0.70 0.26 0.01 --

Table 13: Probability of achieving required number
of journal articles at the end of year 7

Submission Required journal articles
 Interval

 (months) 1 2 3 4 5

 6 1.00 1.00 0.99 0.96 0.88
 7 1.00 1.00 0.97 0.88 0.70
 8 1.00 0.99 0.95 0.84 0.60
 9 1.00 0.98 0.90 0.70 0.41
 10 1.00 0.97 0.85 0.61 0.30
 11 1.00 0.95 0.78 0.49 0.18
 12 0.99 0.94 0.75 0.36 0.13
 13 0.99 0.90 0.63 0.29 0.07
 14 0.98 0.90 0.62 0.26 0.04
 15 0.98 0.84 0.53 0.18 0.03
 16 0.98 0.82 0.46 0.14 0.02
 17 0.96 0.81 0.40 0.08 --
 18 0.96 0.78 0.40 0.11 --

Table 14: Probability of achieving required number
of journal articles at the end of year 8

Submission Required journal articles
 Interval

 (months) 1 2 3 4 5

 6 1.00 1.00 0.99 0.96 0.88
 7 1.00 1.00 0.97 0.89 0.71
 8 1.00 0.98 0.95 0.82 0.60
 9 1.00 0.99 0.90 0.73 0.42
 10 1.00 0.97 0.86 0.63 0.31
 11 1.00 0.95 0.77 0.47 0.19
 12 0.99 0.93 0.74 0.42 0.13
 13 0.98 0.90 0.68 0.30 0.07
 14 0.98 0.89 0.64 0.26 0.07
 15 0.98 0.84 0.55 0.19 0.02
 16 0.97 0.84 0.52 0.15 --
 17 0.96 0.80 0.44 0.12 --
 18 0.96 0.75 0.38 0.06 --