Opinion for the Court filed by Circuit Judge DAVIS.

DAVIS, Circuit Judge:

Sanders, et al. (Sanders) appeal the grant of summary judgment to Washington Metropolitan Area Transit Authority (WMA-TA). The District Court (Penn, J.) held that WMATA was immune from this suit. We affirm, partially on other grounds.

In 1982 appellee WMATA promulgated rules requiring that employees who were involved in on-the-job accidents or unusual operating incidents be escorted by a supervisor to a designated medical facility to be tested for the presence of alcohol, illicit drugs, and controlled substances. Blood samples were taken to detect the presence of alcohol. Two urine tests were performed to test for illicit or controlled drugs: an EMIT test (enzyme immunoassay) and a GCMS test (gas chromatography-mass spectrometry). 1

The eighteen appellants were bus or rail operator employees of WMATA, all members- of the union (Local 689). All had been involved in on-the-job incidents and had submitted to the required blood and urine testing. Each was terminated from employment based on positive results of the post-incident medical examinations. Fourteen of the appellants filed grievances under the collective bargaining agreement *1153 challenging their termination. 2 Eleven of them settled prior to final arbitration and were reinstated with back pay; three proceeded to full arbitration, two of whom were reinstated and granted partial back pay; one’s grievance was wholly denied by the arbitrator and he was not reinstated. Four appellants failed to file grievances or pursue their remedies under the collective bargaining agreement. One of those four was a probationary employee and therefore not eligible to file under the collective bargaining agreement. 3

Appellants brought suit in the District Court claiming that they had been negligently discharged from their employment, and also alleging violation of the Fourth and Fourteenth Amendments, deprivation of their right to privacy, and violation of the Rehabilitation Act of 1973, 4 as well as violation of 42 U.S.C. § 1983. 5 They requested compensatory damages, over and above the back pay granted in the grievance proceedings, in the amount of $500,-000 each for injury arising from humiliation, embarrassment, lost wages, and damage to reputation.

WMATA moved for summary judgment, which the District Court granted, 652 F.Supp. 765. The court concluded that WMATA was entitled to invoke immunity under the Eleventh Amendment and the Compact (creating WMATA) because the activity involved was a governmental function as to which WMATA’s immunity had not been waived.

II.

The parties dispute as to what is before us on this appeal. Appellants argue that their constitutional and § 1983 points — that WMATA’s rule on testing is invalid under the Fourth and Fourteenth Amendments because WMATA requires such testing without specific and objective facts giving reasonable suspicion or probable cause to test the particular employee — have been preserved, as well as the separate claims for negligent termination (because the tests were improperly conducted). WMA-TA counters that appellants have now abandoned their constitutional and statutory points (which were undoubtedly raised below) and that the negligent termination claims are precluded by the results of, or failure to follow, the grievance procedure.

It is true that appellants have not argued the merits of their constitutional and § 1983 claims, but we think they have barely maintained their contentions in their brief (App.Br. 4, 14) when they say that they do not challenge WMATA’s right “to conduct post-incident drug testing of employees suspected of drug or alcohol use ” and testing of employees “suspected, on the basis of specific and objective facts, of drug or alcohol use” (emphasis added). We view this somewhat cryptic observation as sufficient to call upon us to reject WMA-TA’s argument that the appellants’ constitutional and § 1983 claims have been abandoned. 6 Appellants’ contention seems to be that testing could not be conducted unless there was sufficient reasonable suspicion or probable cause relating to the individual employee.

Because these claims are still in the case, we must consider the correctness of the *1154 District Court’s holding that WMATA is immune from suit under the Compact on those contentions. 7 To that problem we now turn.

III.

WMATA was established by an interstate compact (Compact) entered into by Maryland, Virginia and the District of Columbia, which was consented to by Congress. Pub.L. No. 89-774, 80 Stat. 1324 (1966), as amended. 8 Section 80 of the Compact provides (D.C.Code.Ann. § 1-2431 (1981)):

The Authority [WMATA] shall be liable for its contracts and for its torts and those of its Directors, officers, employees and agent committed in the conduct of any proprietary function, in accordance with the law of the applicable signatory (including rules on conflict of laws), but shall not be liable for any torts occurring in the performance of a governmental function.

The District Court ruled that, if any tort was committed through the application to appellants of WMATA’s drug-test rule, that injury “occurred in the performance of a governmental function.”

In Morris v. WMATA, 781 F.2d 218 (D.C.Cir.1986), this court held that (a) the signatories to the Compact, together with Congress, had conferred their respective sovereign immunities (including immunity under the Eleventh Amendment) on WMATA, and those entities had then partially waived those immunities in Section 80 of the Compact; and also that (b) the question whether the function in question is “governmental” or “proprietary” under Section 80 is one of federal law.

The federal concept of a “governmental function” in connection with tort liability was defined authoritatively, prior to adoption of the Compact, in the leading case of Dalehite v. United States, 346 U.S. 15, 73 S.Ct. 956, 97 L.Ed. 1427 (1953), involving the Federal Tort Claims Act, 28 U.S.C. § 2680 (1946). The Court stated that Congress did not contemplate “liability arising from acts of a governmental nature or function” (Id. at 28, 73 S.Ct. at 964) and that “[o]ne need only read § 2680 [the Tort Claims Act] in its entirety to conclude that Congress exercised care to protect the Government from claims, however negligently caused, that affected the governmental functions.” Id. at 32, 73 S.Ct. at 966 (emphasis added). The opinion adds that one way the Tort Claims Act effected that objective was by excepting “acts of discretion in the performance of governmental functions or duty ‘whether or not the discretion involved be abused.’ ” Id. at 33, 73 S.Ct. at 966. And the Court added that “the discretion [is] of the executive or the administrator to act according to one’s judgment of the best course, a concept of substantial historical ancestry in American law.” Id. at 34, 73 S.Ct. at 967.

When the Court came to define the limits of this governmental discretion, the opinion said that it “includes more than the initiation of programs and activities. It also includes determinations made by executives or administrators in establishing plans, specifications, or schedules of operations [footnote omitted]. Where there is room for policy judgment and decision there is discretion.” Id. at 35-36, 73 S.Ct. at 968. This language was recently repeated, and Dalehite reconfirmed, in United States v. Varig Airlines, 467 U.S. 797, 811-12, 104 S.Ct. 2755, 2763-64, 81 L.Ed.2d 660 (1984).

Varig Airlines, itself, says flatly that “[t]he discretionary function exception, embodied in the second clause of § 2680(a), marks the boundary between Congress’ *1155 willingness to impose tort liability upon the United States and its desire to protect certain governmental activities from exposure to suit by private individuals." 467 U.S. at 808, 104 S.Ct. at 2762 (emphasis added). Later in its opinion, the Court described the allegedly negligent acts attacked in Dalehite as "governmental duties" protected against suit under the Tort Claims Act. Id. at 811, 104 S.Ct. at 2763 (emphasis added). Finally, Varig Airlines stressed that "Congress wished to prevent judicial `second-guessing' of legislative and administrative decisions grounded in social, economic, and political policy through the medium of an action in tort. By fashioning an exception for discretionary governmental functions, including regulatory activities, Congress took `steps to protect the Government from liability that would seriously handicap efficient government operations.'" Id. at 814, 104 S.Ct. at 2765 (emphasis added) (quoting United States v. Muniz, 374 U.S. 150, 163, 83 S.Ct. 1850, 1858, 10 L.Ed.2d 805 (1963).

In granting immunity from tort actions to WMATA's "governmental" functions, the Compact seems to us to have accepted the Dalehite conception which we have just outlined. 9 In construing the Federal Tort Claims Act-the federal consent-to-suit on tort claims-Dalehite had, given the definitive understanding of those torts as to which Congress had consented (in that Act) to actions against the Federal Government. The "governmental function" language of the Compact's Section 80 likewise concerns torts, and torts alone. The parallel is apparent, and it is especially appropriate to follow the Congressional understanding, in tort cases, of "governmental function." First, "Congress played a particularly active role in creating WMA-TA," initiated the Compact, and "expressly retain[ed] WMATA's immunity from suit for `torts occurring in the performance of a governmental function.'" Morris v. WMA-TA, supra, 781 F.2d at 222. Second, tort suits involving a "governmental function" are quite dissimilar under Section 80 from suits (including tort claims) involving a "proprietary function" in that the latter (but not the former) are controlled by "the law of the applicable signatory"; the strong inference is that "governmental function" tort suits are to be governed by federal law-as that law has been stated in the Tort Claims Act. 10

The core of the Dalehite idea is that WMATA should be immune-in the words of Varig Airlines-from judicial "second-guessing" via tort suits "of legislative and administrative decisions grounded in social, economic, and political policy" (467 U.S. at 814, 104 S.Ct. at 2765) and from courts' "second-guessing" through private tort suits "the political, social, and economic judgments of an agency exercising its regulatory function." Id. at 820, 104 S.Ct. at 2768. 11

Iv.

In this case the "governmental function" under the Dalehite-Varig principles was the adoption of the general policy *1156 of testing for drugs or alcohol immediately after an on-the-job accident or unusual operating incident. That rule was certainly grounded in the social, political, and regulatory activities of WMATA. For one thing it was founded on the social and regulatory policy of protecting the public, WMATA’s employees, and the users of the WMATA transportation systems from danger. Sections 12(c) and 77 of the Compact expressly gave the Authority the right and duty to make regulations for the safety of the public and its employees. In addition, Section 75 of the Compact directed WMATA to comply with the rules of the “signatories and political subdivisions and agencies thereof” with respect to use of streets, highways, vehicular facilities, and traffic control and regulation; the District of Columbia, Maryland and Virginia all prohibit the operation of vehicles by persons who are intoxicated or drugged. Another “governmental” objective sought by the testing policy was the operation of “improved transit facilities,” mandated by Section 2 of the Compact. Ensuring that all WMATA bus and rail operators are competent to drive, free from drugs or alcohol, is obviously a significant regulatory policy tending toward the goal of “improved transit facilities” — a directive plainly including safety considerations. See Division 241, Amalgamated Transit Union v. Suscy, 538 F.2d 1264, 1267 (7th Cir.), cert. denied, 429 U.S. 1029, 97 S.Ct. 653, 50 L.Ed.2d 632 (1976) (upholding Chicago Transit Authority’s comparable tests for drugs and alcohol); Turner v. Fraternal Order of Police, 500 A.2d 1005, 1008 (D.C.App.1985) (same for police of the District of Columbia).

It necessarily follows that WMATA is immune from suit on all of appellants’ constitutional and § 1983 grounds (Counts I, III, IV of the complaint). These are all general attacks on the testing plan itself, not on the manner of testing in a particular case. These challenges to the testing plan all invoke judicial “second-guessing,” through a tort suit, of “administrative [WMATA] decisions grounded in social, economic, and political policy” — and therefore invoke “governmental” and “regulatory” functions. United States v. Varig Airlines, supra, 467 U.S. at 814, 104 S.Ct. at 2765. The Compact bars such suits and the District Court correctly so held.

The remaining count of the complaint (Count VI) — titled “Negligent Termination” —alleges that WMATA negligently implemented the over-all testing plan by failing to use due care in administering and confirming the tests. This assertion is probably not directed to a “governmental” function because there is no indication in the record that the subordinate employees were directed to be negligent or that they were told specifically how to administer the tests. Nor does any real discretion on the part of the testers seem to have been involved. We assume, therefore, that WMA-TA is not immune from suit under this claim of “negligent termination” which appears to be one of ordinary negligence.

There are, however, other bars revealed by the record. 12 Fourteen of the appellants pursued their grievance remedies and either received relief or (in the case of one appellant) were held not entitled to any relief. On the issue of negligent termination, these appellants are es-topped from litigation by the doctrines of claim preclusion (res judicata) and issue preclusion (collateral estoppel) because the issue of negligent termination was either raised or should have been raised in the grievance process, and therefore cannot be pressed again.

For WMATA employees, including appellants, the claim for “negligent termination” was required to be submitted, if unsettled, to final and binding arbitration. Section 66(c) of the Compact explicitly so declares as to all unresolved “labor disputes” and Congress intended to impose such compulsory arbitration. S.Rep. No. 92-931, 92d Cong., 2d Sess. 9 (1972); H.R. *1157 Rep. No. 92-1155, 92d Cong., 2d Sess. (1972). This court has given the term “labor dispute” in the Compact a broad coverage. Office & Professional Employees Int’l Union v. WMATA, 724 F.2d 133, 137-38 (D.C.Cir.1983). There can be no doubt that appellants had to submit their claim for “negligent termination” to the grievance process. Most of them did so.

A decision in arbitration is normally conclusive in determining an employee’s rights under a collective bargaining agreement. Steelworkers’ Trilogy (United Steelworkers of Am. v. Enterprise Wheel & Car Corp., 363 U.S. 593, 80 S.Ct. 1358, 4 L.Ed.2d 1424 (1960); United Steelworkers of Am. v. Warrior & Gulf Navigation Co., 363 U.S. 574, 80 S.Ct. 1347, 4 L.Ed.2d 1409 (1960); United Steelworkers of Am. v. American Mfg. Co., 363 U.S. 564, 80 S.Ct. 1343, 4 L.Ed.2d 1403 (1960)). The rationale behind this principle is obvious: to permit unrestricted judicial review of the arbitration process would utterly defeat the purpose of finality of arbitration by allowing a second tier of review. Steelworkers v. Enter. Wheel & Car Corp., 363 U.S. at 599, 80 S.Ct. at 1362; Devine v. White, 697 F.2d 421, 435 (D.C.Cir.1983). The grievance process provides the parties with a efficacious, economical, and informal route in resolving labor disputes. In addition, the process itself is more conducive to the preservation of ongoing employment relations than is litigation, and the arbitrator is, in general, more competent than the court in interpreting and implementing collective bargaining agreements. AT & T Technologies, Inc. v. Communications Workers of Am., 475 U.S. 643, 106 S.Ct. 1415, 1419, 89 L.Ed.2d 648 (1986). A smooth continuance of employment relations is particularly vital as it pertains to WMATA because a serious labor dispute is likely to cause a curtailment of transit services. See, e.g., Office & Professional Employees Int’l Union v. WMATA, 724 F.2d 133, 138 (D.C.Cir.1983).

An aggrieved employee is not always barred from a judicial forum but, as this court stated in Office & Prof. Emp. Int’l Union v. WMATA, 724 F.2d at 137: “[t]he case must present some egregious deviation from the norm before we will abandon the firmly-established principles of deference.” This court has also held that the decisions of an arbitrator can have res judi-cata (claim preclusion) or collateral estop-pel (issue preclusion) effect on a subsequent law suit. Schattner v. Girard, Inc., 668 F.2d 1366 (D.C.Cir.1981), so ruled. When the parties have had a full and fair opportunity to present their evidence, the decisions of the arbitrator should be viewed as conclusive as to subsequent proceedings, absent some abuse of discretion by the arbitrator. Restatement (Second) of Judgments § 84(3) (1982); Greenblatt v. Drexel Burnham Lambert, Inc., 763 F.2d 1352 (11th Cir.1985). This court said in Schatt-ner, in upholding the District Court’s grant of summary judgment:

For reasons of judicial economy as well as the policies of federal law, courts tend to look askance at efforts to seek relief beyond that granted in arbitration proceedings. The rules of res judicata and collateral estoppel must govern our review of such proceedings if we are to advance the goal of promoting arbitration as an alternative to the complications and costs of litigation. Because arbitration is to be encouraged, courts appropriately uphold awards and preclude additional claims that were or should have been submitted to arbitration.

668 F.2d at 1371 (citations omitted).

Schattner also made the same ruling for “claims that should have been submitted to arbitration, even if they were not actually heard.” Id. at 1368 (emphasis in original).

There is no claim that the grievance process was unfair or flawed. The result must be that the fourteen appellants who filed grievances have had their “negligent termination” claims decided already, and those decisions preclude renewed and repeated litigation in the current case. Moreover, eleven of these appellants each executed a settlement agreement declaring that “the parties have reached a mutually satisfactory resolution” of that appellant’s grievance. These settlement agreements *1158 further support preclusion of the current claims of the employees who signed them.

Four of the appellants never pursued the grievance process at all. We have already discussed in this Part, supra, the requirement of the Compact — supported by the clear intent of Congress — that all “labor disputes” be resolved through the grievance process, including compulsory arbitration (if necessary). Thus, under settled law the WMATA employees who failed to exhaust the grievance and arbitration proceedings, available to them, may not seek redress in court on claims that could and should have been grieved. Republic Steel Corp. v. Maddox, 379 U.S. 650, 653, 85 S.Ct. 614, 616, 13 L.Ed.2d 580 (1965); Allis-Chalmers v. Lueck, 471 U.S. 202, 220-21, 105 S.Ct. 1904, 1916, 85 L.Ed.2d 206 (1985); National Treasury Employees Union v. Kurtz, 636 F.2d 411 (D.C.Cir.1980).

One of the four who did not invoke the grievance process was a probationary employee (with less than 90-days service) and under the bargaining agreement he did not have access to grievance proceedings. But, as in the federal civil service system, WMATA was permitted, under the collective bargaining agreement, to discharge him (as a probationer) “at its own discretion”; no “sufficient cause” for termination was required. Accordingly, that probationary employee has no judicial claim for “negligent termination.”

For these reasons, the judgment of the District Court is

Affirmed.

. Local 689 of the Amalgamated Union (Local 689), on behalf of the WMATA bus and train operations it represented, filed a grievance (under its collective bargaining agreement) protesting the establishment of the rule. The grievance was arbitrated (as required by the agreement if a dispute cannot be settled) and was denied.

. As we have indicated, the collective 'bargaining agreement between the union and WMATA requires WMATA to submit all unresolved labor disputes between WMATA and union employees to final and binding arbitration. See Part V, infra.

. Under the terms of the collective bargaining agreement, WMATA may discharge new employees during a probationary period of ninety days, and no grievance can be claimed by the union. See Part V, infra.

. 29 U.S.C. § 701 et seq.

. 42 U.S.C. § 1983 provides in pertinent part:

Every person who, under color of any statute, ordinance, regulation, custom, or usage of any State ... subjects, or causes to be subjected, any citizen of the United States or other person within the jurisdiction thereof to the deprivation of any rights, privileges, or immunities secured by the Constitution and law, shall be liable to the party injured in an action at law, suit in equity, or other proper proceeding for redress.

.Appellants make no mention of their claims under §§ 503 and 504 of the Rehabilitation Act of 1973, which the District Court rejected; we hold therefore that those claims have been abandoned.

. We do not consider whether those appellants who pursued the grievance procedure or settled under it — and were reinstated and received back pay — are precluded from bringing this suit simply because they received relief in the grievance arbitration process. Cf. Alexander v. Gardner-Denver Co., 415 U.S. 36, 46 n. 5, 51 n. 14, 94 S.Ct. 1011, 1018 n. 5, 1021 n. 14, 39 L.Ed.2d 147 (1974) (involving suit under Title VII of the Civil Rights Act of 1964 where the employee’s claim was rejected in arbitration). In any event, there would be some appellants who did not pursue a grievance proceeding or failed to prevail there.

. The Compact is codified at District of Columbia Code sections 1-2431 — 1-2436.

. We recognize that the Dalehite-Federal Tort Claims Act test and the "governmental-proprietary" test are viewed as distinct and not necessarily coterminous (Restatement (Second) of Torts § 895C comments e and g; Prosser and Keaton on Torts 1953 (5th ed. 1983); Spencer v. General Hospital, 425 F.2d 479, 488 (D.C.Cir.1969) (Wright, I., concurring); cf. yang, 467 U.S. at 812, 104 S.Ct. at 2763), but the "discretionary function" standard is at least a subset of "governmental functions." As the Restatement, supra, puts it (~ 895C comment g), the former test "is based on the theory that some governmental functions are of a type that should not be subject to review and second-guessing by the courts in a tort decision."

. The ,legislative history of the Compact sheds no light on the meaning and scope of "governmental function."

. In Owen v. City of Independence, 445 U.S. 622, 100 S.Ct. 1398, 63 L.Ed.2d 673 (1980), the Supreme Court held that § 1983 suits could be brought against municipalities, despite the common-law doctrine of a "governmental" exception often applicable to municipalities, because the states and the federal government had abolished (with respect to § 1983 actions) "whatever vestige of the State's sovereign immunity the municipality possessed." Id. at 647-48, 100 S.Ct. at 1413. For WMATA, the Compact specifically preserved, instead of abolishing, that fount of immunity. See Morris v. WMATA, supra, 781 F.2d at 222.

. These issues were not reached by the District Court but they were raised below and the record is sufficient for us to resolve them. See, e.g., Tymshare, Inc. v. Covell, 727 F.2d 1145, 1150 (D.C.Cir.1984).