I % - . % *

3

APPLICATION OF QUEUING THEORY TO ON-ORBIT LOGISTICS

David P. Mar t in , I1 Science Appl i c a t ~ o n s I n t e r n a t i o n a l Corporat ion

Colorado Springs, CO 80906

ABSTRACT

Models t o analyze o n - o r b i t maintenance and support o f space veh ic les have looked a t on ly a p o r t i o n o f the o v e r a l l problem o f t r anspo r ta t i on , se rv i c i ng and ground support o f space-based assets. Th is has caused problems i n understanding the complexi ty o f o n - o r b i t support and hindered s tud ies i n t o the cos t -e f f ec t i veness of t he bene f i t s o f o n - o r b i t support versus cu r ren t support methods. Using a technique p rev ious l y app l i ed t o an ana lys is o f t he Space Shu t t l e , on-orb i t model i n g can be performed from a systems perspect ive w i t h a v a i l able queuing models t o help answer c r i t i c a l quest ions on resource u t i l i z a t i o n , success r a t e , and t ime expendi ture requ i red t o perform on-orb i t l o g i s t i c s support. Bene f i t s from g rea te r f l e x i b i l i t y and expandab i l i t y are achieved us ing t h e queuing theory technique.

JNTRODUCTION

Models are t o o l s used t o represent something i n t he r e a l world. Models can be as s imple as a l i n e drawing on paper o r as complex as h i g h - f i d e l i t y f l i q h t s imula tors . Models are b u i l t f o r many purposes, one o f which i s t o analyze and eva iuate t he c a p a b i l i t i e s t o per form o n - o r b i t l o g i s t i c s support f o r space veh ic les . These models are main ly computer s imu la t i on models t h a t employ a v a r i e t y o f d i f f e r e n t techniques and languages.

Problem Statement. Models t o analyze on -o rb i t maintenance and support o f space veh i c l es have no t captured the o v e r a l l problem o f t ranspor ta t ion , s e r v i c i n g and ground support o f space-based assets. Th is has caused problems i n understanding the complex i ty o f o n - o r b i t support and hindered s tud ies i n t o t he cos t -e f f ec t i veness o f t he b e n e f i t s o f on- o r b i t support versus cu r ren t support methods.

Puroose. The purpose o f t h i s paper i s t o evaluate t h e use o f queuing theory t o analyze o n - o r b i t l o g i s t i c s support from a systems perspect ive and show how some o f the bas i c problems o f modeling on- o r b i t l o g i s t i c s can be overcome. Fo l lowing a b r i e f background i n t o t he p r i nc ip les /app l i c a t i o n s o f queuing theory, t h i s paper g ives an example o f a queuing theory model used t o assess the Space Shut t le , exp la ins t h e appl i c a t i o n o f queuing theory t o o n - o r b i t l o g i s t i c s models, and summarizes t h e b e n e f i t s o f t h e use o f queuing theory t o t h i s prob l em.

Copyr ight 1988 by SAIC. Publ ished by t he American I n s t i t u t e o f Aeronaut ics and Ast ronaut ics , Inc . w i t h pern iss ion.

BACKGROUNQ

To ensure a common understanding o f queuing theory, t h i s sec t ion s ta tes t he d e f i n i t i o n and terminology o f queuing theory and g ives severai app)rications, i nc lud ing a d e t a i l e d example o f the use of queuing theory as p rev ious l y app l ied t o the Space Transpor ta t ion System. This example l ays the groundwork by which the o n - o r b i t l o g i s t i c s model can be both constructed and understood.

D e f i n i t i o n o f Oueuins Theorv. Queuing Theory i s def ined i n Turban and Meredi th (7 ) as: " the theory a n ~ l i ed t o t he oroblem o f f i n d i n q the appropr ia te - 7 7 . - - -

l e v e l o f serv ices" t o prov ide to-customers i n a p r a c t i c a l , c o s t - e f f i c i e n t manner.

Basic Terminoloqy. The queuing theory model ( 7 ) i s composed o f f o u r s p e c i f i c par ts : t h e customer, the a r r i v a l process, t he se rv i ce f a c i l i ty/process, and the queue i t s e l f . Each o f these terms are ex- p l ained here.

Customer. Customers are def ined as those i n need o f t h e se rv i ce the system provides. Customers can be people, machines, raw mater ia ls , e t c .

A r r i v a l Process. The a r r i v a l process i s the manner i n which customers come t o the serv ice f a c i l i t y / p r o c e s s . No d i f f e r e n t i a t i o n need be made here as t o whether the customer comes t o the f a c i l i t y o r the process comes t o t he customer, a l though i t i s t y p i c a l l y thought t h a t the customer " a r r i v e s " a t the se rv i ce f a c i l i t y .

Serv ice F a c i l i tv /Process. The se rv i ce i s whatever t he customer needs t o have performed. Th is se rv i ce can be performed by a person (e.g., a bank t e l l e r ) , a machine (a gaso l ine pump), o r a space (park ing l o t ) . If the se rv i ce can o n l y be performed a t a p a r t i c u l a r l oca t i on , a f a c i l i t y i s associated w i t h t he service.

The Oueug. Whenever the customer f i n d s t h a t t he serv ice i s no t ava i l ab le because i t i s busy o r unava i lab le f o r any reason, a queue i s formed i n which the customer i s w a i t i n g f o r serv ice . Wait ing l i n e s i n grocery s tores and banks are the most common queues, bu t people w a i t i n g f o r a plumber o r o the r repairman can a lso be considered wa i t i ng i n a queue f o r serv ice .

A ~ ~ l i c a t i o n s o f Oueuina Theory. Several d i f f e r e n t modeling techniques, each based on queuing theory, have been app l i ed t o a v a r i e t y o f problems. Modeling techniques such as those descr ibed i n P r i t s k e r (S), have been used t o analyze a i r c r a f t maintenance scheduling, assembly l i n e s , bank t e l l e r s , d i s t r i b u t i o n systems, m i l i t a r y l o g i s t i c s , maintenance scheduling, mining operat ions, r a i l road d ispatch ing, t r a f f i c l i g h t i n g systems, ambulance serv ices and p o l i c e response systems design. Most o f these app l i ca t i ans are s p e c i f i c app l i ca t i ons o f

queuing theory in that there is a customer who needs a service from an organization. Once the need has been satisfied, the customer leaves the system, returning when the service is once again needed. This approach is very attractive for modeling logistics systems, because there is a customer, a service and resources/facil i ties that are used to perform this service. Once the number of resources and time used in service have been computed, it becomes much simpler to compute the cost of the support system. A specific example foilows to show how a queuing theory model has been appi ied.

SPECIFIC EXAMPLE OF OUEUING THEORY UTILIZA~ION

The author's major experience with queuing theory models was with the logistics assessment model of the Space Transportation System (STS) using Pritsker and Pegden's Simulation Language for Alternative Modeling (SLAM) (5). As part of the logistics assessment team, the Air Force Opera- tional Test and Evaluation Center (AFOTEC) built a model of the entire ground operations and logistics system for the STS. This section describes the approach, methodology and output results of the model to lay the groundwork for the on-orbit model.

Aooroach. The STS is an extremely large system with many variables that open the system to various methods of modeling. The approach selected by AFOTEC was to use the systems approach used by Beer ( Z ) , Forrester (3) and others. In this approach, the system is first bounded, then a top-level model is constructed of the basic system. This top-level model is expanded into further detail as the accuracy and significance of the variables within the system are defined. This approach, which Beer describes as "Cones of Resolution," allows the modeler to work down into finer levels of granular- ity until an understanding of the nature of the system is found and system performance can be eval- uated. Because the STS was such a large system, the systems approach was used with the major end- product to be the determination of the STS flight rate.

Methodoloay. Once the approach was selected, the model was bounded and an initial system model was built. The STS was defined as eight segments (see Figure 1): (1) the Space Shuttle Vehicle (SSV) . (i .e., External Tank (ET), Sol id Rocket Boosters (SRBs) and the Orbiter); (2) the Kennedy Space Center (KSC) Launch and Landing System; (3) the Vandenberg AFB Ground Support System; (4) the Mission Control Center at Johnson Space Center (JSC) (including training, simulation and flight planning resources); (5) the Air Force-developed Inertial Upper Stage; (6) the Payload Integration Facility at KSC for DoD payloads; (7) the Air Force Controlled Mode at JSC for controlling clas- sified STS missions; and (8) the contractor facilities for ET production and SRB manufacture/- refurbishment. The first model included only the SSV, KSC and the Contractor Facil i ties. Simp1 ify- ing assumptions were made about the other segments so that the modeler could ensure that the segments were modeled correctly. Then, the model was expanded to include the remaining segments. Further detail was needed to model the interplay between the SSY and +ts ground operations, so detailed submodels were built of KSC ground

SPACE TRANSPORTATION

SYSTEM

I

NASA SEGMENTS DO0 SEGMENTS

SPACE ! VANDENBERG 1 1 SHUTLE I I G.SO!JNO SUPPORT VEHICLE I SEGMENT

LANDING SYSTEM INERTIAL UPPER STAGE

JSC CONTROLLED

CONTRACTOR FACILITIES INTEGRATION

FIGURE 1. STS SEGMENTS

operations, relaxing some of the assumptions used in previous models concerning a success-oriented schedule, no delays due to equipment failures and the readiness of spare parts. Results from the submodels were processing times and resource utilizations that were fed into the top-level model to see how STS operations zt KSC interacted with the functions at JSC, VAFB and the contractor facilities.

Outouts. The model computed resource util ization, waiting times for services or resources, and, most importantly, the flight rate. The impacts of these results could then be compared through sensitivity analyses to determine the critical elements of the STS. It should be noted that results from the top- level model as early as 1980 predicted a maximum flight rate of 13-14 launches/year from KSC and pointed to overall vehicle assembly, not Orbiter, operations, as the critical service in the overall ground flow.

ON-ORBIT OUEUING MODE4

The approach used in the STS model ing was used to determine how well this approach would work on the problem of on-orbit support . To do this, a basic approach was out1 ined, followed by an analysis of considerations to successfully build such a model. The model itself was constructed using the SLAM symbology. Finally, expansions that would be necessary to bring the model up to a full systems approach were analyzed for feasibility.

Basic Aooroach. The systems approach was first applied to the on-orbit queuing model. Since the "system" could be defined very restrictively (i.e., only the Satellite Vehicles (SVs) and the Orbital Maneuvering Vehicle (OMV)) or very openiy (i.e, the SVs, OMV, a1 1 repair resources, the launch systems and ground repair facilities), an initial model of the restrictive case was constructed using scme

s i m p l i f y i n g assumptions about t h e o t h e r p a r t s o f t h e system. Then, t h e model was expanded i n t o t h e t o t a l systems envi ronment. The Background s e c t i o n d e f i n e d f o u r elements o f a queuing system: t h e Customer, A r r i v a l Process, S e r v i c e F a c i l i t y l P r o c e s s and t h e Queue. I f queuing theory -can be a p p l i e d t o o n - o r b i t l o g i s t i c s , each o f these elements shou ld be p r e s e n t .

Customer. The Customer f o r an o n - o r b i t model would be t h e SV i t s e l f . A v a i l a b i l i t y o f t h e SV t o p e r f o r m i t s m i s s i o n would be t h e key measure o f t h e i o g i s t i c s system t h a t woula suppor t t h e SYs i n a p a r t i c u l a r s a t e l 1 i t e c o n s t e l l a t i o n o r s e t o f c o n s t e l l a t i o n s .

A r r i v a l Process. The A r r i v a l Process would be more a k i n t o t h e p o l i c e d i s p a t c h i n g o r ambulance s e r v i c e r a t h e r than t h e more t r a d i t i o n a l customer e n t e r i n g t h e s e r v i c e f a c i l i t y (as w i t h banks, gas s t a t i o n s , o r maintenance f a c i l i t i e s ) . I n t h e on- o r b i t model, t h e a r r i v a l process would be based on t h e SVs Mean Time Between C r i t i c a l F a i l u r e s (MTBCF) o r expend i tu re o f f u e l , e t c . T h i s would cause a reques t f o r s e r v i c i n g t o e n t e r t h e system. The reques t would be answered by severa l p o s s i b l e responses, e.g.:

Go r e c o v e r t h e SV, r e p l a c e i t w i t h an o p e r a t i o n a l spare, and r e t u r n t h e SV t o t h e maintenance f a c i l i t y ;

Go t o t h e SV, f i x i t , and t h e n go t o t h e n e a r e s t f a i l e d Sy o r r e t u r n t o t h e l o g i s t i c s "base, be i t a Space S t a t i o n , t h e O r b i t e r o r p o s s i b l y t h e Ear th ;

Replace t h e SV w i th a p r e p o s i t i o n e d spare and w a i t f o r t h e n e x t a v a i l a b l e oppor tu - n i t y t o r e c o v e r / r e p a i r t h e f a i l e d SV.

Changing scenar ios i s c r i t i c a l t o b o t h unders tand ing and d e s i g n i n g t h e system. There fo re , expansions t o t h e model, d iscussed below, w i l l demonstrate how t h e model can be changed.

S e r v i c e Fac i 1 i ty/Process. The s e r v i c e process i s t h e key e lement f o r o n - o r b i t l o g i s t i c s . Here, t h e process i s r e s t o r i n g t h e SV. As d iscussed above, t h i s can ba p e r f o m e d i n p lace , a t ano ther f a c i l i t y ( i . e . , t h e Space S t a t i o n o r O r b i t e r ) , o r a t a maintenance f a c i l i t y on Ear th . The model shou ld be a b l e t o change t o suppor t analyses o f each o f these o p t i o n s and o t h e r s t h a t become apparent th rough t h e a n a l y s i s process.

The Oueue. The Queue f o r t h e o n - o r b i t model e x i s t s o n l y i n t h e p r i o r i t i e s p l a c e d on f i x i n g t h e SV. Time spent w a i t i n g t o be f i x e d can be spent e i t h e r i n s i t u o r i n a maintenance shop. Regard- l e s s , t h e t i m e i s t h e key f a c t o r , because t h i s i s t i m e t h a t i s not spent s u p p o r t i n g t h e miss ion . K r e l l ( 4 ) d e f i n e s v e r y w e l l t h e r e l a t i o n s h i p between t h e c o n s t e l l a t i o n o f SVs and t h e number necessary t o suppor t t h e miss ion . Once t h e number o f a c t i v e SVs drops below t h i s number, t h e system can be cons idered i n o p e r a t i v e . The c r i t i c a l t a s k t h e o n - o r b i t l o g i s t i c s system must per form, then, i s t o m a i n t a i n t h e c o n s t e l l a t i o n a t o r above t h i s opera i iona : l e v e l . From t h i s d i s c u s s i o n , i t i s e v i d e n t t h a t t h e o n - o r b i t l o g i s t i c s problem f i t s i n t o a c l a s s i c a l queuing t h e o r y approach. The n e x t s e c t i o n d iscusses t h e c o n s i d e r a t i o n s f o r deve lop ing a methodology u s i n g queu ing theory .

Cons idera t ions . To p r o p e r l y c o n s t r u c t an o n - o r b i t l o g i s t i c s model, c e r t a i n c o n s i d e r a t i o n s had t o be answered. These c o n s i d e r a t i o n s were how t o model maneuvers, SV f a i l u r e s and t h e d e c i s i o n r u l e s .

Maneuvers. Maneuvers h o l d t h e key t o per fo rm- i n g o n - o r b i t l o g i s t i c s support , because t h e a r r i v a l process i s not as s imp le as jumping i n t o t h e ambulance and making a h o u s e - c a l l . Bates e t . a1 (1) d e s c r i b e t h e b a s i c problem o f maneuvers from one o r b i t t o t h e n e x t u s i n g t h e equat ion f o r change i n v e l o c i t y , which i s :

where,

9 = Change i n v e l o c i t y = V e l o c i t y o f p r e l i m i n a r y o r b i t -

vp> = Change i n o r b i t a l p l a n e

F o r example, i f t h e OMV must maneuver f rom t h e Space S t a t i o n o r b i t ( i n c l i n a t i o n = 27O) t o a p o l a r o r b i t , w i t h t h e r i g h t ascension h e l d cons tan t , t h e change i n v e l o c i t y i s equal t o t h e v e l o c i t y o f t h e OMV i n t h e Space S t a t i o n o r b i t ! T h i s equat ion would have t o be a p p l i e d f o r each SV when c o n s i d e r - i n g how much I would be r e q u i r e d t o maneuver from one o r b i t t o t i e f a i l e d SV. F o r t u n a t e l y , a s i m i l a r problem w i t h t h e A n t i s a t e l l i t e system r e q u i r e d AFOTEC t o mod i fy an e x i s t i n g FORTRAN-language sub- r o u t i n e which modeled s a t e l l i t e mot ion over t ime. T h i s s u b r o u t i n e was used t o d e s c r i b e t h e SV mot ion and q u i c k l y update t h e SV p o s i t i o n . A s i m i l a r program c o u l d be used t o model SV mot ion i n an on- o r b i t l o g i s t i c s program and de te rmine how much f u e l would be r e q u i r e d f o r an OMV t o reach t h e f a i l e d SV f rom e i t h e r an O r b i t e r , t h e Space S t a t i o n , o r ano ther SV p o s i t i o n , i f t h e OMV was a l ready i n use. By d e f i n i n g t h e f u e l r e m a i n i n g on t h e OMV and c a r r y i n g t h i s as an a t t r i b u t e o f t h e OMV so t h a t d e c i s i o n s t o move t h e OMV would be based on whether o r n o t i t c o u l d reach t h e f a i l e d SV, an a c c u r a t e r e p r e s e n t a t i o n o f s e r v i c i n g i n t h e c o n t e x t o f s a t e l l i t e mot ion c o u l d be b u i l t .

F a i l u r e s . Many p r e v i o u s models o f l o g i s t i c s systems use " c l o c k s " t o d e s c r i b e when t h e f a i l u r e o f t h e system w i l l occur . T h i s approach randomly s e l e c t s t h e t i m e t o f a i l u r e f rom t h e assumed f a i l u r e d i s t r i b u t i o n (a Monte C a r l o s i m u l a t i o n ) and causes an i n p u t t o t h e l o g i s t i c s systems a t t h a t t ime. Whi le t h i s techn ique adequate ly descr ibes t h e f a i l u r e process, ano ther process i s needed t o m o n i t o r t h e impact o f f a i l u r e s on t h e o v e r a l l system. There fo re , a pseudo-resource was used t o m o n i t o r when t h e s a t e l l i t e s were a v a i l a b l e and when t h e y were non-mission capable. I n t h i s manner, t h i s t o t a l u t i l i z a t i o n o f t h e pseudo-resource (expressed as a percentage o f t i m e ) would a l l o w an i n s t a n t r e a d i n g on t h e o v e r a l l a v a i l a b i l i t y o f t h e c o n s t e l l a t i o n .

D e c i s i o n Rules. The b a s i s f o r d e t e r m i n i n g when, where, and who would respond t o t h e f a i l e d SV was ano ther problem. Since t h e numbers on t i m e t o f a i l u r e would be r e a d i l y a c c e s s i b l e i n t h e model, t h e q u e s t i o n o f " P e r f e c t I n f o r m a t i o n " arose ( i . e., would t h e schedu le r f o r o n - o r b i t maintenance know t h e e x a c t c o n d i t i o n o f each SV o r subsystem w i t h i n t h e SV and be a b l e t o schedule more t h a n one r e p a i r a c t i o n f o r each SV o r a!! SVs i n t h e same o r b i t a l p l a n e ? ) . I f t h e schedu le r would have a l l t h i s

i n f o r m a t i o n , s imp le FORTRAN subrou t ines c o u l d be b u i l t t o schedule maintenance a c t i o n s based on a p r i o r i t y system and send on t h e SV s e r v i c e r o n l y those i tems n e c e s s i r y f o r s e r v i c i n g . Since t h i s can be cons idered t o o p e r f e c t " a case, some o f t h i s i n f o r m a t i o n was n o t used i n t h e schedu l ing d e c i s i o n r u l e s . However, i t was e v i d e n t t h a t s imp le FORTRAN subrou t ines , which a r e used i n t h e SLAM methodology, can be used t o model o n - o r b i t suppor t d e c i s i o n r u l e s .

Basic O n - O r b i t L o g i s t i c s Model. The i n i t i a l model i s shown i n F i g u r e 2. T h i s model uses t h e SLAM symbology f o r queues, a c t i v i t i e s , b r a n c h i n g and matching, b u t i s expanded so t h a t those mfar7i i : iar w i t h SLAM can understand how t h e model works. B a s i c a l l y , t h e model f i r s t p l a c e s t h e SV c o n s t e l l a - t i o n i n t o i t s p r o p e r o r b i t . Then, based on t h e SV's MTBCF, t h e SVs f a i l and r e q u i r e s e r v i c i n g . A t t h i s p o i n t , a d e c i s i o n r u l e s u b r o u t i n e i s used t o de te rmine how, when and by whom t h e s e r v i c e w i l l be s u p p l i e d . Once t h e d e c i s i o n has been made, t h e OMV i s tasked and, once a v a i l a b l e , reaches t h e SV and per fo rms t h e ma in tenance /serv ic ing . A t t h i s p o i n t , t h e SV r e t u r n s t o o p e r a t i o n a l s t a t u s w h i l e a second d e c i s i o n r u l e decides i f t h e OMV shou ld move t o i t s n e x t f a i l e d SV o r r e t u r n t o base.

E x ~ a n s i o n s . S i x d i f f e r e n t areas were subsequent ly cons idered as areas f o r expansion t o b r i n g t h e i n i t i a l On-Orb i t L o g i s t i c s Model up t o i t f u l l c a p a b i l i t i e s . These s i x areas a r e d iscussed below.

SV Subsvstems. By mode l ing t h e SV as a s e t o f subsystems i n s t e a d o f a s i n g l e e n t i t y , b e t t e r d e f i n i t i o n o f c o n s t e l l a t i o n a v a i l a b i l i t y . S ince SVs w i l l n o r m a l l y degrade over t i m e i n s t e a d o f f a i l t o t a l l y , t h i s i s a more accura te r e p r e s e n t a t i o n o f t h e r e a l w o r l d , The expansion o f t h e model i s shown i n F i g u r e 3. The f i r s t l i n e o f t h e i n i t i a l model would be r e p l a c e d w i t h t h e code shown i n F i g u r e 3 t o make t h e e n t i r e expanded model. T h i s f i g u r e uses t h e same " c l o c k " p r i n c i p l e used above, excep t t h a t each SV subsystem now has i t s own c l o c k . Each

c l o c k i s checked d a i l y t o see if a f a i l u r e has occur red . When a f a i l u r e happens, i t i s checked t o see if i t i s a minor problem t h a t can be "worked around" (e.g., a redundant u n i t w i t h i n a subsys- tem). I f so, a l o w - p r i o r i t y maintenance event i s scheduled so t h a t when t h e OMV i s c l o s e t o t h e SV, maintenance can be performed. However, i f t h e f a i l u r e causes l o s s of t h e SV c a p a b i l i t y , t h e SV i s removed f rom t h e a c t i v e c o n s t e l 1 a t i o n and an immediate maintenance even t i s scheduled. T h i s example has been expanded i n some d e t a i l t o show t h e ease w i t h which t h e model can be expanded as more d e t a i l i s r e q u i r e d . T h i s i s one o f t h e b e n e f i t s o f u s i n g e x i s t i n g t o o l s such as SLAM. The model i s e a s i e r t o ad jus t j change jupdate , as t h e a n a l y s i s r e q u i r e s .

O r b i t a l Reolacement U n i t s and E x ~ e n d a b l e s f o r S&. Once SV subsystems are modeled, t h e model can be expanded t o i n c l u d e t h e use o f O r b i t a l Replace- ment U n i t s (ORUs) and expendables such as f u e l . When t h e subsystems modeled above f a i l , t h e d e c i s i o n r u l e would now be based on b o t h t h e a v a i l a b i l i t y of a s e r v e r w i t h t h e a p p r o p r i a t e ORU on hand t o p e r f o r m t h e maintenance. T h i s expansion s t a r t s t o t a k e i n t o account t h e ground system and i t s impact on o n - o r b i t support , because r e s u p p l y o f ORUs/expendables f rom t h e ground can now be i n c l u d e d so t h a t u t i l i z a t i o n o f r e s u p p l y v e h i c l e s can be determined.

Replace SV and Return Oot ion. As ment ioned above, changing t h e suppor t s t r a t e g y t o see t h e impac t on l o g i s t i c s suppor t i s c r i t i c a l when t r y i n g t o p l a n f o r such an endeavor. There fo re , t h i s model c o u l d i n c o r p o r a t e as p a r t o f t h e a n a l y s i s a d i f f e r e n t d e c i s i o n r u l e where z n - o r b i t spares a r e p r e p o s i t i o n e d or k e p t a t some i n t e r m e d i a t e f a c i l i t y , " such as t h e Space S t a t i o n . When a f a i l u r e occurs, t h e o n - o r b i t spare i s p o s i t i o n e d and a c t i v a t e d , w h i l e t h e f a i l e d SV i s scheduled f o r p i c k - u p and r e t u r n e d t o a maintenance f a c i l i t y f o r r e p a i r . The r e p a i r e d SY then becomes t h e new on- o r b i t spare. The key t o u s i n g e x i s t i n g techn iques

OMV I FH

SV AWAITS REPAIR

RETURN SV TO 'OR- STATUS

FIX SV

COLLECT OMV MODEL

OMV

FIGURE 2. INlTlAL MODEL

L

SICK

sv + 1 1 DAY FAILURE

SV AWAITS REPAIR

POPULATION ORBIT FAILURE CLOCKS

FIGURE 3. EXPANDED MODEL

CLOCKS B CHECK

such as SLAM t o perform these analyses i s t h a t the t o o l s a v a i l a b l e g i v e the modeler the f i e x i b i l i t y t o ad jus t t h e model q u i c k l y and e a s i l y . For example, an ex tens ive ana l ys i s on the e f f e c t s o f when t o move SRBs from KSC and i t s a f f e c t on turnaround was performed q u i c k l y by changing a s i n g l e number. Th is f l e x i b i l i t y a l lows more t ime t o analyze opt ions and exp lore a l t e r n a t i v e s r a t h e r than t r y i n g t a f i g u r e out how t o reprogram user -def ined models. Th is f l e x i b i l i t y i s a key t o t h e use o f queuing theory i n o n - o r b i t support modeling.

Fuel o r Soares Storaae C a ~ a c i t y . When ORUs and expendables are added t o t he model, t he next s t e o i s t o model f u e l and ORU storaqe capac i ty on- o r b r t t o - ~ r o o e r l y s i z e t he l o g i s t i c : system requ i red b n - b r b i i . Once again, t h i s i s a s imple t ask o f e s t a b l i s h i n g a Storage Resource, r h i c h i s used up as spares/ fuels are brought up t o o r b i t and re leased as these same a r t i c l e s are taken ou t t o r e s t o r e a f a i l e d SV. I n a l i k e manner, t he need f o r an SRB Processing and Staging F a c i l i t y was found very e a r l y on i n t h e STS l o g i s t i c s ana lys is . By adding t h i s resource, us ing two a d d i t i o n a l nodes, and moving the SRB processing tasks over t o t h i s new f a c i l i t y , i t was easy t o see t h e marked impact t h a t use o f t h i s f a c i l i t y would have on o v e r a l l turnaround t ime. The same technique, . appl i e d t o on-orb i t l o g i s t i c s , determines the need f o r such a f a c i l i i y and would he lp s i z e t he f a c i l i t y , too.

Ground Systems Suooort f o r On-Orbit Loq i s t i cs . Once the o n - o r b i t system i s de f i ned t o t h i s l e v e l , t h e next step would be t o add t h e ground systems; i .e . , maintenance f a c i l i t i e s , launch veh i c l es and t h e i r r espec t i ve ground opera t ions . These are c r i t i c a l elements, because the resourcas modeled so f a r have a l l assumed adequate ground t ranspo r ta t i on . U l t ima te l y , however, t he f a i l u r e o f SVs causes demands on the o n - o r b i t support system which, i n t u rn , p laces demands on the launch systems t o

resupp ly them. By i nc lud ing the launch systems i n L l l r : L.- model, even s t a r t i n g a t a macro-level w i t h the number o f launch veh ic les and t h e i r respect ive processing times, i t would be poss ib le t o see the i n t e r p l a y between the ground and on-orb i t systems and ga in a b e t t e r understanding o f the t ime i t takes f o r a f a i l e d SV t o place a demand on the launch system, cons ider ing the o n - o r b i t system as the necessary qu i ck - reac t i on server, o r ambulance d r i v e r .

Jmoact o f New Enqine Desians. F i n a l l y , the model should be ab le t o handle new designs. One o f t h e major problems i n o n - o r b i t l o g i s t i c s i s the amount o f f u e l r equ i red t o perform the maneuvers necessary t o move from one o r b i t t o the next . As i l l u s t r a t e d i n F igure 4, even two Global Pos i t ion- i n g System s a t e l l i t e s w i t h t he same i n c l i n a t i o n , a l t i t u d e and pe r i od have v a s t l y d i f f e r e n t o r b i t s because t h e i r r i g h t ascension a) i s changed 120°. However, suppose t h e fue l consumption c r i t e r i a i n t h e model i s changed. Then the impact o f h i gh ISp engines on t h e l o g i s t i c s system's c a p a b i l i t y t o support cou ld be determined. Th is new Isp could then become a design requirement f o r a new OMV, thus p rov id ing the j u s t i f i c a t i o n t o s t a r t work on a new OMV.

SUMMARY

The ana l ys i s presented here has shown t h a t queuing theory can be app l ied t o t he problems o f on-orb i t l o g i s t i c s , Since there are several commercial t o o l s ava i l ab le which r e a d i l y perform queuing theory s imulat ions, these t o o l s can be used t o e f f e c t i v e l y model the o n - o r b i t l o g i s t i c s problem. Furthermore, s ince these t o o l s prov ide g rea te r f l e x i b i l i t y i n expanding/ref in ing the modeling e f f o r t , queuing theory modeling should be considered as a pr imary t o o l i n the search f o r answers t o the quest ions o f how t o best perform o n - o r b i t l o g i s t i c s support .

REFERENCES

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2. Beer, Stafford. Decision and Control. John Wiley & Sons, Ltd., New York, 1978.

3. Forrester, Jay W . industria7 Dvnamics. Massachusetts Institute of Technology. Mii Press, Cambridge, MA, 1977.

4. Krell, Bruce E. "Cost-Effectiveness Measures of Replenishment Strategies for Systems of Orbital Spacecraft." RAND Corporation, Santa Monica, CA, December 1979.

5. Pritsker, A. Alan 8. Modelina and Analvfit Usinq 0-GERT Networks. Pritsker & Associates, Inc. John Wiley & Sons, New York, 1977.

6. Pritsker, A. Alan 8. and Claude Dennis Pegden. Introduction to Simulation and SLAM. Pritsker & Associates, Inc. John Wiley & Sons, New York, 1979.

7. Turban, Efrain and Jack R . Meredith. Fundarnen- tal s o f Manaaement Science. Florida International University. Business Publ ications, Inc. Dallas, TX, 1977.