A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures N. Blefari-Melazzi and G. Reali
University of Perugia, Perugia (Italy) E-mail: {blefari,reali}@diei.unipg.it Abstract Current satellite systems operate according to circuit switching transfer modes. To improve flexibility and efficiency, several kinds of packet switching systems have been proposed. However, it appears that full packet switches are still too complex and expensive to be implemented on board the satellites, in the mid-term. For the time being, a compromise has been found in satellite networks with Dynamic Bandwidth Allocation Capabilities (DBAC). Such systems are based on classical circuit switches, but the DBAC payload allows changing dynamically the capacity of each connection, without the need of tearing-down and setting-up again the connection itself. In this paper we consider a DBAC satellite system and define algorithms to allocate the bandwidth in such a way as to provide performance guarantees and to exploit efficiently the system resources. We assume that the overall traffic is divided into high priority (HP) traffic and low priority (LP) traffic. A given amount of resources is assigned to the HP traffic so as to satisfy pre-defined performance measures. When the HP traffic is not employing all the allocated capacity, the unused capacity is temporarily taken away from the HP traffic and used to carry LP traffic. The HP traffic loading the system is regulated by means of Dual Leaky Buckets (DLBs). We define bandwidth-handling policies, design Connection Admission Control rules and evaluate analytically the system performance. Keywords: Satellite communications, Dynamic Bandwidth Allocation, guaranteed performance, Dual Leaky Bucket, Connection Admission Control rules, performance evaluation. This work has been supported by the European Union in the framework of the ACTS program (project ASSET, AC326).
Corresponding Author: Nicola BLEFARI-MELAZZI Dipartimento di Ingegneria Elettronica e dell’Informazione (DIEI) Università degli Studi di Perugia Via G. Duranti 93 - 06125 Perugia - ITALY Tel: +39 075 585 2630 +39 075 585 2654 E-mail:
[email protected]
N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
1
Introduction
This work has been carried out in the framework of the ACTS program ASSET (ACTS Satellite Switching and End to End Trials), sponsored by the European Union. ASSET will demonstrate the core capabilities of a satellite network, the so-called EuroSkyWay Network [LOS98]. The EuroSkyWay (ESW) Network is composed of: • a certain number of GEO satellites • a Master Control Station (MCS) • user terminals (mobile) • earth stations (fixed), including a certain number of Interworking Units (IWU); these IWUs are stations that interface the ESW system with terrestrial networks (e.g. the Internet, ATM, etc.). In addition to its own protocols, which allow ESW users to exchange information among themselves, the ESW system is designed to support a variety of terrestrial protocols. The ESW system plays the role of bearer service for different communication paradigms, such as ATM, the Internet, N-ISDN, POTS and so on. The IWUs of EuroSkyWay allow also communications between ESW users and other users belonging to the above mentioned terrestrial networks. Current satellite systems operate according to circuit transfer modes. To improve flexibility and efficiency, several kinds of packet switching systems have been proposed [e.g. TOL98, BAI96]. However, it appears that full packet switches are still too complex and expensive to be implemented on board the satellites, in the mid-term. In addition, circuit switching has still some attractions, at least for particular services. For instance, ESW can support very easily the N-ISDN, the POTS and CBR video services. Internet Service Providers can use ESW connections to transport aggregated Internet traffic, with a significant gain in terms of simplicity and overhead, if compared to IP on ATM. For the time being, a compromise between circuit and packet transfer modes has been found in satellite networks with Dynamic Bandwidth Allocation Capabilities (DBAC). Such systems are based on classical circuit switches, but the DBAC payload allows changing dynamically the bandwidth of each connection, without the need of tearing-down and setting-up the connection itself. The ESW network is a DBAC system. The procedure used to set-up ESW connections involves the MCS; therefore the signalling information has to make two satellite hops to go from a terminal to the MCS and come back. Once a connection is set-up, the Dynamic Bandwidth Allocation Capabilities allow changing the bandwidth of the connection itself by means of In Band Requests (IBRs). Each terminal can ask to increase or decrease dynamically the capacity of a connection, according to his needs. The IBRs are sent to a module resident in the satellite and called Traffic Resource Manager (TRM). The TRM can accept or not the IBRs. When a user requests a change of capacity, the new value of capacity is effective only after that he receives an acknowledgement from the TRM. Since the MCS is not involved in the latter procedure, such acknowledgement reaches the user after one round trip time. Thanks to the DBAC, the ESW remains a fairly simple system (the on-board switch is a simple T-switch) and yet it can offer increased efficiency and flexibility. In this paper, we define a resource management scheme that guarantees the user perceived performance and exploits the system resources efficiently. We consider the ESW system but our
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
results are applicable to any DBAC system, if terrestrial so much the better, since the performance of our scheme improves when the round trip time decreases. The proposed resource management scheme is based on the following assumptions. The overall traffic is divided into high priority (HP) traffic and low priority (LP) traffic. A given amount of resources is assigned to the HP traffic so as to satisfy pre-defined performance measures. When the HP traffic is not employing all the allocated capacity, the unused capacity is temporarily taken away from the HP traffic and used to carry the LP traffic. When the HP traffic needs the capacity that has been taken away, said capacity is once again given back to the HP traffic itself, after a round trip time. Obviously, these variations of the capacity actually used by the HP traffic are performed by means of the DBAC mechanism. The HP traffic is regulated before entering the system by means of Dual Leaky Buckets (DLBs). The DLBs ease the tasks of the Connection Admission Control since their output process, that is the traffic entering the system, has known characteristics. The DLBs can be used also to smooth the incoming traffic in order to make its statistic profile compliant with the characteristics of the ASSET bearer service. In this work, we define bandwidth-handling policies, design Connection Admission Control rules and evaluate analytically the system performance. A complete simulation package has been developed to evaluate the overall system performance with reference to the above points and to validate the analytical results. The structure of this paper is as follows. In Section 2 we introduce the resource management scheme and define the bandwidth-handling policies. Section 3 is concerned with the system performance evaluation. In Section 4, we present selected numerical investigations while some concluding remarks are given in Section 5.
2
Resource management scheme
The user traffic is transferred in the form of “satellite cells”. The satellite cell payload has a length of 53 bytes and can contain a full ATM cell or other user-generated data (IP datagram (part of), X.25 packet (part of), 53 samples of a continuous PCM stream, etc.). A common framing structure is defined and applied to all the carriers, both in the uplink and in the downlink direction. The transfer mode is based on circuit switching. The smallest unit switched within the system is the satellite cell. Each satellite cell (or Frame Unit, FU) provides a net information rate of 16000 bit/s (basic channel). One frame contains n FUs with n depending on the terminal type and on the traffic direction (the resulting bit rate ranges from 0.160 Mbit/s to 524.288 Mbit/s). Independently by the station type, the frame duration is constant and equal to 26.5 ms. Each connection can use a number of FUs ranging from 1 to n so that the relevant capacity varies from 16 kbit/s to n X16 kbit/s. The capacity of each circuit can be changed dynamically frame by frame, in steps of one basic channel (i.e. 16000 bit/s). In the following, we consider a generic satellite terminal (this can be a mobile terminal, a fixed earth station or an InterWorking Unit, IWU) and we assume that this terminal intends to generate a given amount of traffic towards the satellite network. This traffic can be either endogenous or coming from external networks. The terminal requires to the Master Control Station a suitable connection; the MCS exerts a Connection Admission Control (CAC) and eventually accepts the requested connection. Given the circuit switching transfer mode, if the bit rate of the incoming traffic is not constant, a significant amount of resources can be wasted. In the following
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
we assume that the offered traffic is (at least in part) a Variable Bit Rate one (VBR), otherwise there is no need to consider improvements to a pure circuit switching way of operation. The modification of the capacity assigned to a connection may occur frame by frame by means of “In Band Requests” (IBRs) made to the satellite TRM. When a terminal asks for a change of capacity, the new value of capacity is effective only after that the terminal itself has received a positive answer from the satellite. The latency of the proposed scheme is then equal to one round trip time, ∆T. We intend to make use of the DBAC scheme to improve the efficiency in the resource utilisation while providing performance guarantees. In other words we want to design a resource management scheme such that: 1 the system resources are used only when effectively needed; 2 the Quality of Service (QoS) perceived by the users is always the contracted one. If we allowed all the users to modify at will the capacity of their connection then we could reach a high efficiency but there would be no guarantee that a given user always obtains the capacity that he needs. Such guarantee requires instead a suitable CAC scheme, including a Traffic Descriptors (TD) Declaration and a Usage Parameter Control (UPC). The issue is then very similar to the congestion control in the framework of the B-ISDN/ATM, which has motivated a very large research effort in the last years. In our case, the issue is even more complex because we have to take into account the DBAC scheme and the system latency. To overcome such difficulties and to simplify the system procedures we make two assumptions: 1) the overall traffic is divided into high priority traffic (HP) and low priority traffic (LP). A given amount of resources is assigned to the HP traffic so as to satisfy pre-defined performance. When the HP traffic does not use the allocated capacity, the unused portion is lent to the LP traffic. When the HP traffic needs the capacity that has been taken away, said capacity is once again given back to the HP traffic itself, after a round trip time. Obviously, these variations of the capacity currently used by the HP traffic are performed by means of the DBAC. 2) the HP traffic entering the system is regulated by means of Dual Leaky Bucket (DLB) shapers. A DLB implements jointly two Generic Cell Rate Algorithms (GCRA) [ITU96, ATM96]. Such GCRAs assure that the traffic entering the system can be characterised by only four parameters and simplify greatly the three phases of a traffic control scheme, namely the Traffic Descriptors Declaration, the CAC and the UPC. The four parameters controlled by a DLB are: the Peak Cell Rate (PCR) and its Cell Delay Variation Tolerance (CDVTPCR), the Sustainable Cell Rate (SCR) and its tolerance (CDVTSCR); the latter includes the so-called Burst Tolerance (BT). In this way, we can control the effects of the DBAC scheme on the performance perceived by the HP traffic and guarantee such performance. We also assume that each terminal has a buffer of size B (cells), used by the HP traffic (HP buffer). If various traffic sources, belonging to the same terminal, want to emit traffic towards the same destination, then they can be statistically multiplexed over the same ESW connection. In any case, each HP traffic source is regulated by a DLB shaper. The proposed system architecture is shown in Fig. 1. The HP traffic generated by a given terminal and supported by the same ESW connection can be a superposition of K heterogeneous traffic sources. In Fig. 1 we assumed also an additional buffer for the LP traffic (LP buffer), even if
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
this is not strictly necessary. The capacity not used by the HP traffic of the considered terminal can be used by LP traffic belonging to the same terminal or to other terminals. Note that we make a distinction between traffic sources and terminals. This distinction is useful mainly in the case of fixed and IWUs stations where several traffic sources require the transport services of the ESW system and the latter can satisfy such requests by means of a single ESW connection, if the involved traffic sources share the same destination. The traffic control methodology is similar to the one of the ATM and to the RSVP paradigms. All the HP users (traffic sources) belonging to a given terminal and willing to transmit traffic, declare to the terminal itself a set of Traffic Descriptors (i.e. the DLB parameters), which describe the traffic that the users intend to generate. Based on such TDs, the terminal requests the MCS to establish a ESW connection with a capacity equal to C cells/s. Given the circuit switching transfer mode of the ESW system, this means that the terminal requests a circuit with capacity C. The MCS executes a Connection Admission Control and accepts or denies the terminal request. During the transfer phase, the user traffic is policed to control that it adheres to the traffic contract established during the preceding phase (by means of the DLBs). When the number of HP users (traffic sources) supported by a given terminal varies, the terminal negotiates with the MCS a new value of C, by means of set-up and tear-down signalling procedures. The negotiated capacity, C, is shared between HP and LP traffic in a dynamic way by means of the DBAC scheme. The capacity actually used by the HP traffic is then a function of time, C(t), varying between a minimum value, Cmin, and a maximum value, C. The value of the capacity actually used in a given time is negotiated with the TRM by means of the IBRs. The LP traffic can use the remaining capacity C- C(t). The utilisation of such remaining capacity is controlled by appropriate algorithms, which will not be addressed in this paper, for space limitations. Summing up, the capacity negotiated with the MCS varies only when new sources are added or existing sources conclude their activity. The capacity actually used by the HP traffic of a given terminal varies during the transfer phase, even if the number of supported HP sources is constant. The MCS accepts connection requests until the sum of the relevant capacities is less than or equal to the overall capacity of the involved links. From the point of view of the MCS, there are no more functions to be performed. On the contrary, from the terminal point of view, we have to design a methodology to choose the values of the system parameters so that the HP users perceive the desired performance. For instance, given K sources, an HP buffer of size B and the TDs of each supported HP source, we might want to determine the value of the capacity of the ESW connection, C such that the requirements of the HP users in loss and delay are satisfied. Inversely, given C, B and the TDs of each HP traffic source we could be interested in determining the value of K such that the admitted users are pleased with the perceived performance. The former case is generally called a dimensioning problem while the latter one is referred to as definition of CAC rules. For the sake of simplicity, in the following we will generally speak of CAC rules, being obvious that the same rules can be used both for dimensioning and for resource allocation purposes. These CAC rules are the essential point of our scheme. In fact, given the system latency, the HP traffic of a given terminal can not always use immediately the capacity that it needs and that the terminal has negotiated. This means that the values of C, B and K must be suitably chosen, as a function of the TDs of the HP traffic sources and of the delay and loss performance requested by the HP traffic. This applies also when a connection supports only one HP
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
source. In fact, a single HP source can experience loss and delay, even if the capacity requested during the set-up of the ESW connection is equal to its Peak Cell Rate. This is because the capacity of the ESW connection is not always entirely available (or immediately available after an IBR), owing to the adopted DBAC scheme and to the system latency. In the past years, countless CAC rules have been proposed in the literature and different sets of TDs have been assumed. Thanks to the significant simplification implied by the use of the DLBs, the problem has become simpler. An elegant solution to the CAC problem is proposed in [ELM97]. In [ELM97] the Authors consider a generic network element, composed by a statistical multiplexer with a FIFO queue, fed by traffic sources regulated by means of DLBs. With reference to such network element, they design simple CAC rules that allows guaranteeing Quality of Service (QoS) requirements in loss and delay. To define our CAC rules we start from the ones envisaged in [ELM97] and we suitably modify them. The main difference between our system and the one considered in [ELM97] is that the server of the HP traffic in our system goes on vacation according to a given law (to be described in the following). In other words, the HP server capacity is not constant but it varies dynamically, with a latency equal to the round trip time, ∆T. The detailed (logical) steps of the proposed resource management scheme are (we refer to a single ESW connection, supported by a given terminal): 1) each HP source wishing to emit traffic declares its TDs to the terminal to which it belongs. All the traffic sources characterised by the same TDs are said to belong to the same class; each terminal can support J traffic classes. 2) the terminal, wishing to emit HP traffic, requires the MCS to set-up a connection (circuit) with a capacity equal to C cells/s; this connection can support a superposition of K traffic sources or only one source. The value of C is chosen by means of the CAC rules to be defined in the following. Inversely, given an existing allocated capacity equal to C, the terminal accepts up to K requests made by traffic sources, with K evaluated by means of the same CAC rules; 3) the MCS exerts its peak allocation strategy and accepts or denies the connection request; 4) if the connection request is accepted, the terminal may start to emit HP traffic; 5) the emitted traffic is regulated by DLBs, one for each traffic source; 6) if the terminal becomes aware of needing less capacity to transport HP traffic, because of the VBR nature of the supported traffic, it declares so to the TRM module resident in the satellite, by means of an In Band Request (negative IBR); 7) after releasing a given HP capacity, if the terminal needs again a greater capacity for the HP traffic, it requests said capacity to the TRM by means of an In Band Request (positive IBR); the new value of capacity may be used by the terminal only after that the latter has received a positive answer from the satellite; this happens after one round trip time, since the MCS is not involved; 8) each HP traffic source (that is, each end-user) has always the right to emit information, according to his traffic contract, expressed in terms of his TDs; this means that even when the HP contracted capacity is not used, it may be required at any time; 9) the satellite can always accept the IBRs, both positive and negative; this is possible thanks to the (to be defined) CAC rules and to the DLB regulators of the incoming traffic; 10) the capacity released by the HP users is used to carry LP traffic;
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
11) when HP users need again the contracted capacity, the capacity temporarily assigned to LP traffic users is taken away from the latter and given back to the former; 12) the LP users have no guarantee of receiving a given amount a capacity, they only use the portion left by HP users; 13) eventually, a fraction of the overall capacity can be not assigned to HP users and left always available to LP users. Thanks to this way of operation, the overall efficiency can be greatly increased, especially in presence of very bursty HP traffic. Finally, we remark that we have assumed that the so-called CAC rules are implemented in the terminals while the MCS executes only operations related to a classical circuit switching scheme. A different solution could be to implement also such CAC rules in the MCS, thus simplifying the terminals. In this case, the “connection request” messages must contain the TDs of each supported HP traffic source, the performance measures requested by each HP source and the size of the HP buffer of each terminal. To complete the definition of this scheme we must describe how and when a terminal decides to request more capacity to transport HP traffic or to release a portion of the capacity that it is has been using for the HP traffic. In other words, we must define the law followed by the HP server to go on vacation and we have to establish how the capacity of a connection is alternatively used by HP and LP traffic. To this aim, we assume that the value of C(t), that is the capacity being used by the HP traffic, is chosen as a function of the content of the HP buffer (see Fig. 1). The remaining capacity, C-C(t), is offered to the LP traffic. It is clear that C(t) must be a non-decreasing function of the HP buffer content: when the content of such buffer increases, the HP traffic requires more capacity and viceversa. We considered several laws of variation of C(t), as a function of the HP buffer occupancy, v(t) [TECH_R]. In this paper, we will use only one of them, the so-called “One step without hysteresis”. The IBRs requesting a given capacity are therefore a function of v(t) and are generated periodically, with a period Tupd. The choice of the latter parameter is a trade-off between signalling&processing load and responsiveness of the algorithm. However, in the ESW system: • the satellite TRM can change the capacity assigned to a given terminal only at times integer multiple of a Frame duration time; • the IBRs are transported in a field of the header of the ESW Frame Unit, so that each Frame Unit can carry an IBR without affecting the signalling load; We then assume Tupd equal to a frame duration time, with the additional rule that an IBR is effectively transmitted only if it is different from the previous one. The assumed law of variation of C(t), as a function of the HP buffer occupancy, is shown in Fig. 2. When v(t) is less than a given threshold v0, the capacity assigned to the HP traffic is equal Cmin; when v(t) is greater or equal to v0 than C(t)=C. Note that the system latency introduces an intrinsic hysteresis that helps to avoid possible instabilities of the capacity assignment algorithm. 2.1
System modelling We consider a generic terminal and, for the sake of simplicity and without loss of generality, we assume that all the HP traffic sources belong to the same class (homogeneous sources). The following results can be extended to the heterogeneous sources case. With reference to the traffic coming out from a generic DLB and feeding the HP buffer (see Fig. 1) we denote as: • Ps: the peak rate (in cells/s);
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
rs: the sustainable rate (in cells/s); • BTS: the burst tolerance (or token buffer size). We also assume that the Cell Delay Variation Tolerances, both CDVTPCR and CDVTSCR, are equal to zero or somehow included in the other parameters. We also let: • B: the HP buffer size (in cells); • v(t): the HP buffer occupancy, at the time instant t (in cells); • C: the overall capacity allocated by the MCS to the considered terminal (in cells/s); • K: the number of HP sources supported by the same ESW connection; • Π: the cell loss probability suffered by the HP traffic; • C(t): the capacity used, at the time instant t, by the HP traffic belonging to the considered connection of a given terminal (in cells/s); • C-C(t): the capacity left unused by the HP traffic belonging to the considered connection of a given terminal and available to carry LP traffic at the time instant t (in cells/s); • ∆T: the delay for putting into effect the capacity assignment command, mainly due to the round trip time of the satellite link (in seconds); • CAV: the long term average value of the capacity left available to carry LP traffic, equal to E[C-C(t)] (where E[x] denotes the expected value of x) (in cells/s); • CAV,N: CAV normalised with respect to the maximum theoretical value of the same quantity: •
C AV, N =
E [C - C (t )] C - Krs
( Eq. 1 )
ρTOT: the total utilisation factor of the considered link; • DMAX: the maximum delay perceived by the HP users in the HP buffer; • C(v): a generic law of variation of C(t) as function of the HP buffer occupancy, v(t); The aim of this system modelling is to design the CAC rules for our system. For comparison purposes, we define also a Reference system. Such system is a plain circuit switching one, without DBAC capabilities, where the bandwidth assigned to each terminal can not be varied dynamically by means of IBRs. In such system several sources can be statistically multiplexed in a given terminal, by using the CAC rules defined in [ELM97]. In the Reference system each connection transports only one kind of traffic (in our terminology, all the capacity of the connection is permanently assigned to the HP traffic). The server that models the link capacity of the Reference system does not go on vacation and it is constantly available to transport HP traffic, i.e. C(t ) = C, ∀ t . No LP traffic is transported. The objective of our approach is to go forward by exploiting the capacity left unused by the HP traffic. If we use the same system parameters and the same number of HP sources of the Reference system, while, at the same time, trying to reap some capacity by means of the DBAC, it is clear that the performance of the HP traffic will tend to worsen. This is due to the system latency, ∆T. In addition, the adopted capacity assignment algorithm results in a lower value of the average capacity used to deliver HP traffic, with respect to that of the Reference system. It can also be shown that, when ∆T tends to zero, the performance perceived by the HP traffic, in terms of throughput and loss, are unaffected by the DBAC scheme. In other words, such performance tends to that of a system without DBAC, when the system latency tends to zero. •
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
Since we do not want to impair the HP traffic performance, we are faced with different options: • decrease the number of supported HP sources • increase the HP buffer size • increase the allocated capacity, C. In the following, to limit the possible cases and the length of this paper, we will not consider the third option. In any case, the results obtained with reference to the increase of the buffer size can be easily adapted also to the increase of the allocated capacity. We will compare the performance of our approach with that of the Reference system with the following methodology: 1. we set case study parameters for the loss and delay requirements relevant to the HP traffic and for the parameters of the Reference system, B and C; 2. we determine how many HP sources (K) can be allocated in the Reference system, satisfying the above requirements; 4. at this point we have three options: a) if we do not want to increase the buffer space of our terminal, then we have to decrease the number of supported HP sources with respect to the Reference system; in this case the maximum delay suffered in our system is greater than that relevant to the Reference system, because of the lower value of the average capacity usable by the HP traffic; (the two systems have the same buffer space, B, but our system allocates less HP sources than the Reference system: K–∆K); b) if we want to allocate the same number of HP sources in our system, then we have to increase the buffer space of our terminal; in this case the maximum delay suffered in our system is greater than that relevant to the Reference system; (both systems support the same number of HP sources, K, but our system has a greater buffer size than the Reference system: B+∆B); c) if we want both the loss performance and the maximum delay to be equal in both systems, then we have to decrease the number of HP sources in our system; correspondingly the HP buffer space will decrease too; 6. in any case, we pay something but we can transport also LP traffic, in addition to the HP one; 7. after choosing one of the above options, it is possible to quantify the advantages (increase of the total traffic, LP+HP) and disadvantages (decrease of HP traffic or increase of system resources) brought about by our approach. Another way to see this comparison procedure is the following. Our system has a mean value of the capacity usable by the HP traffic that is less than that of the Reference system and less than the maximum value, C. If we want that the HP traffic keeps on enjoying the same performance of the Reference system, then a suitable amount of buffer space must be dedicated to the compensation of the system latency. Let ∆B denote the amount of buffer space that must “compensate” both the lower value of the average capacity used by the HP traffic and the system latency, ∆T. The buffer space ∆B can be added to B and, in this case, we can allocate the same number of HP sources than in the Reference system (case b). Otherwise, ∆B can be seen as a part of the overall buffer size B, which is dedicated to the above compensation. In this case, the buffer that remains to handle the “pure” multiplexing of
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
the HP sources is lower (B-∆B) and less HP sources (∆K) can be supported than in the Reference system (case a). The parameter ∆B will be referred to as ∆BOUT, when added to B (case b) and as ∆BIN, when considered as a part of B (case a). In the following sub-section we derive CAC rules such that loss phenomena are completely avoided at the HP buffer (lossless multiplexing). We also relaxed this requirement and allowed small losses, up to a pre-specified amount (statistical multiplexing), but the relevant results are not reported here for space limitations. 2.2
Allocation rules We first determine the size of the “compensation” buffer space, ∆B. Let us consider a generic function C(v), used to assign the capacity to the HP sources on the basis of the buffer occupancy, v. We assume the token buffer of the shapers to be full at the initial time of a busy period, ti. During the busy period, the following relation applies:
d (v(t )) = KPs − C (v(t − ∆T )), dt
t i ≤ t ≤ t* =
BTS Ps − rs
( Eq. 2 )
Without loss of generality we may assume ti=0. The solution of the above differential equation allows determining ∆B. In fact, by integrating (Eq. 2) in the interval [0, t≤ti] we obtain: t
( Eq. 3 )
v(t ) = KPs t − ∫ C (v(t − ∆T ))dt 0
Since KPs>C, the maximum of v(t) is reached for t=t*:
( ) = KPst
vt
*
*
t*
− ∫ C (v(t − ∆T ))dt = KPs t − *
0
t * − ∆T
∫ C (v(τ))dτ
( Eq. 4 )
− ∆T
where τ=t−∆T. Were all the capacity C always available to the HP traffic, as in the Reference system, we would obtain:
()
vc t* = ( KPs − C ) t*
( Eq. 5 )
On the contrary, our system needs an additional buffer space, with respect to the Reference system, to guarantee the absence of losses; this additional buffer space is equal to:
( ) ( ) = Ct
∆B = v t − vc t *
*
*
t*
− ∫ C (v(t − ∆T ))dt
( Eq. 6 )
0
The above relation shows that the value of ∆B depends, by means of an integral relation, on the capacity assignment law, C(v). Therefore we must choose a specific law in order to evaluate ∆B and to define the CAC rules. However, it can be shown that, by choosing suitably the parameters of one specific law (the “One step without hysteresis”, presented in Fig. 2), it is possible to obtain the same value of ∆B implied by whatever other law one may choose. In fact, if we are willing to use a
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
compensation buffer space of size equal to a value ∆B, then the only requirement that we have to satisfy is that the average value of the capacity C in the interval [0, t*] is: t*
( Eq. 7 )
∫ C (v(t − ∆T ))dt
Ct = 0
t*
=C−
∆B t*
The condition in Eq. 7 can be satisfied by an appropriate choice of the parameters of the assumed law (i.e. v0 and Cmin). This result derives from Eq. 6. All this means that, as far as the size of the compensation buffer is concerned, we can restrict ourselves to use always the same capacity assignment law (the “One step without hysteresis”), without loss of generality. We are now interested to see if the same property applies also to other system parameters, such as: • the number of acceptable HP sources, K; • the maximum delay perceived by the HP users in the HP buffer, DMAX. If that were the case, we could avoid considering different laws of capacity assignment and we could carry out all the comparison procedures defined above by using always the same law. In the following, we will refer to such property as to the Law Independence property, or LI property. We have seen that the LI property applies to ∆B. We now check if the LI property applies also to the number of acceptable HP sources, K. To this end we have to distinguish if our system and the Reference system have the same total buffer size or not. Let us consider the first case (the case (a) of the comparison procedure presented above). The quantity ∆B is a part of the overall buffer size B. A connection witch capacity C can support less HP sources than in the Reference system (∆K) and the parameter ∆B will be referred to as ∆BIN. Let c and b denote the effective bandwidth and buffer allocation, respectively, of the HP sources [ELM97]. In this case: C B − ∆B IN = =K c b
( Eq. 8 )
Since we want to avoid loss phenomena at the HP buffer (we are considering a lossless multiplexing), the following relation must hold [ELM97]:
Ps − c BTS = b Ps − rs
( Eq. 9 )
From (Eq. 8) and (Eq. 9) we obtain:
(KPs − C )t*
= B − ∆B IN
( Eq. 10 )
Eq. 10 shows the dependence of K only on ∆BIN, therefore all considerations on the LI property on ∆BIN also apply to K. Let us now consider the case (b) of the comparison procedure presented above, when both systems support the same number of HP sources, K. In this case, it is evident that K does not depend
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
on the capacity assignment law since ∆BOUT is added to B and it has no effect on the number of HP sources that may be supported. Therefore we can conclude that the LI property always applies to K. The LI property does not apply, in general, to the maximum delay, DMAX. However, if a given requirement on DMAX can be satisfied by adopting the law “One step without hysteresis”, then, given its simplicity and the fact that the LI property applies to all the remaining performance measures of interest, we can always adopt such law, without loss of generality. On the other side, we verified that this law can satisfy a wide range of values of DMAX. For these reasons, in the remainder of this paper, we consider only the above capacity assignment law. Thanks to such assumption we can first particularise the relations given above and then design the CAC rules. We recall that we assume as initial conditions full token buffers. By expressing the above equations as a function of the parameters of the assumed law (i.e. v0 and Cmin) we get: t ≤ t 0 + ∆T v(t ) = ( KPs − C min )t , v(t ) = ( KPs − C min )(t 0 + ∆T ) + (KPs − C )(t − t 0 − ∆T ),
( Eq. 11 ) t 0 + ∆T < t ≤ t*
t − ∆T ≤ t 0 v(t − ∆T ) = (KPs − C min )(t − ∆T ), v(t − ∆T ) = (KPs − C min )t 0 + (KPs − C )(t − t 0 ), t 0 < t − ∆T ≤ t * − ∆T where t 0 =
( Eq. 12 )
v0 is the first time when the threshold v0 is reached. KPs − C min
Substituting Eq. 11 and Eq. 12 in Eq. 4 we obtain
( ) = KPst
vt
*
*
t0
t * − ∆T
− ∆T
t0
− ∫ C min dτ −
(
* * ∫ Cdτ = KPs t − Cmin (t 0 + ∆T ) − C t − ∆T − t 0
)
( Eq. 13 )
and Eq. 6 becomes
() ()
v0 ∆B = v t* − vc t* = (C − C min )(t 0 + ∆T ) = (C − C min ) + ∆T KPs − C min
( Eq. 14 )
Fig. 3 shows a graphic representation of the compensation buffer size, ∆B; in this figure the curves v1(t) and v2(t) are given by: v1 (t ) = (KPs − C ) t
(KPs − C min )t , v2 (t ) = v 2 (t1 ) + (KPs − C )t ,
( Eq. 15 )
0 ≤ t ≤ t1 t1 ≤ t ≤ t 2
( Eq. 16 )
B where t1 = t 0 + ∆T , and t* = TS is the time when the token buffers become empty. Ps − rs With these results, we can derive the CAC rules, starting from the case a) of the comparison procedure. To this aim, we must determine the unknown quantities c, b, K, and ∆BIN, by means of the following system of equations (which collects Eq. 8, Eq. 9, and Eq. 14):
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N. Blefari-Melazzi, G. Reali: “ A Resource Management Scheme for Satellite Networks with Dynamic Bandwidth Allocation Procedures ”
v0 + ∆T ∆B IN = (C − C min ) KPs − C min P −c s B =b Ps − rs TS C B − ∆B IN = b c C c = K
( Eq. 17 )
This non-linear system is relatively easy to solve, even if the relevant solutions are somehow cumbersome. The only care that must be taken is to verify the range of physical acceptability of the mathematical solutions provided by Eq. 17: these must be such that ∆B
